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The Mathematical Work of Wolfgang Schmidt

  • Hans Peter Schlickewei
Part of the Developments in Mathematics book series (DEVM, volume 16)

Abstract

Wolfgang Schmidt’s mathematical activities started more than fifty years ago in 1955. In the meantime he has written more than 180 papers – many of them containing spectacular results and breakthroughs in different areas of number theory.

2000 Mathematics subject classification

11-02 

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Publications by W. Schmidt

  1. 1.
    Über höhere kritische Determinanten von Sternkörpern. Monatsh. Math. 59, 274–304 (1955)Google Scholar
  2. 2.
    Eine neue Abschätzung der kritischen Determinante von Sternkörpern. Monatsh. Math. 60, 1–10 (1956)Google Scholar
  3. 3.
    Eine Verschärfung des Satzes von Minkowski-Hlawka. Monatsh. Math. 60, 110–113 (1956)Google Scholar
  4. 4.
    with K. Baumann: Quantentheorie der Felder als Distributionstheorie. Nuovo Cimento X. Ser. 4, 860–886 (1956)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Mittelwerte über Gitter. Monatsh. Math. 61, 269–276 (1957)Google Scholar
  6. 6.
    The measure of the set of admissible lattices. Proc. Am. Math. Soc. 9, 390–403 (1958)Google Scholar
  7. 7.
    Mittelwerte über Gitter. II. Monatsh. Math. 62, 250–258 (1958)Google Scholar
  8. 8.
    Flächenapproximation beim Jacobialgorithmus. Math. Ann. 136, 365–374 (1958)Google Scholar
  9. 9.
    On the convergence of mean values over lattices. Can. J. Math. 10, 103–110 (1958)Google Scholar
  10. 10.
    Maßtheorie in der Geometrie der Zahlen. Acta Math. 102, 159–224 (1959)Google Scholar
  11. 11.
    On normal numbers. Pac. J. Math. 10, 661–672 (1960)Google Scholar
  12. 12.
    A metrical theorem in geometry of numbers. Trans. Am. Math. Soc. 95, 516–529 (1960)Google Scholar
  13. 13.
    A metrical theorem in diophantine approximation. Can. J. Math. 12, 516–529 (1960)Google Scholar
  14. 14.
    Zur Lagerung kongruenter Körper im Raum. Monatsh. Math. 65, 154–158 (1961)Google Scholar
  15. 15.
    Stetige Funktionen auf dem Torus. J. Reine Angew. Math. 207, 86–95 (1961)Google Scholar
  16. 16.
    Bounds for certain sums; a remark on a conjecture of Mahler. Trans. Am. Math. Soc. 101, 200–210 (1961)Google Scholar
  17. 17.
    Continuous functions defined on product-spaces. Proc. Am. Math. Soc. 12, 918–920 (1961)Google Scholar
  18. 18.
    Über die Normalität von Zahlen zu verschiedenen Basen. Acta Arith. 7, 299–309 (1962)Google Scholar
  19. 19.
    Two combinatorial theorems on arithmetic progressions. Duke Math. J. 29, 129–140 (1962)Google Scholar
  20. 20.
    Simultaneous approximation and algebraic independence of numbers. Bull. Am. Math. Soc. 68, 475–478 (1962)Google Scholar
  21. 21.
    On the Minkowski-Hlawka theorem. Ill. J. Math. 7, 18–23 (1963)Google Scholar
  22. 22.
    Correction to my paper “On the Minkowski-Hlawka theorem”. Ill. J. Math. 7, 714 (1963)Google Scholar
  23. 23.
    Metrical theorems on fractional parts of sequences. Trans. Am. Math. Soc. 110, 493–518 (1964)Google Scholar
  24. 24.
    Über Gitterpunkte auf gewissen Flächen. Monatsh. Math. 68, 59–74 (1964)Google Scholar
  25. 25.
    Normalität bezüglich Matrizen. J. Reine Angew. Math. 214/215, 227–260 (1964)Google Scholar
  26. 26.
    Ein kombinatorisches Problem von P. Erdős und A. Hajnal. Acta Math. Acad. Sci. Hung. 15, 373–374 (1964)Google Scholar
  27. 27.
    Metrische Sätze über simultane Approximation abhängiger Größen. Monatsh. Math. 68, 154–166 (1964)Google Scholar
  28. 28.
    Über simultane Approximation algebraischer Zahlen durch Rationale. Acta Math. 114, 159–206 (1965)Google Scholar
  29. 29.
    On badly approximable numbers. Mathematika 12, 10–20 (1965)Google Scholar
  30. 30.
    On badly approximable numbers and certain games. Trans. Am. Math. Soc. 123, 178–199 (1966)Google Scholar
  31. 31.
    Simultaneous approximation to a basis of a real number-field. Am. J. Math. 88, 517–527 (1966)Google Scholar
  32. 32.
    Maßtheorie in der Geometrie der Zahlen. Colloq. Int. Centre Nat. Rech. Sci. 143, 225–229 (1966)Google Scholar
  33. 33.
    On heights of algebraic subspaces and diophantine approximations. Ann. Math. (2) 85, 430–472 (1967)Google Scholar
  34. 34.
    On simultaneous approximations of two algebraic numbers by rationals. Acta Math. 119, 27–50 (1967)Google Scholar
  35. 35.
    Some diophantine equations in three variables with only finitely many solutions. Mathematika 14, 113–120 (1967)Google Scholar
  36. 36.
    with H. Davenport: Approximation to real numbers by quadratic irrationals. Acta Arith. 13, 169–176 (1967)zbMATHMathSciNetGoogle Scholar
  37. 37.
    with H. Davenport: A theorem on linear forms. Acta Arith. 14, 209–223 (1968)zbMATHMathSciNetGoogle Scholar
  38. 38.
    Asymptotic formulae for point lattices of bounded determinant and subspaces of bounded height. Duke Math. J. 35, 327–339 (1968)Google Scholar
  39. 39.
    Irregularities of distribution. Q. J. Math. Oxf. II. Ser. 19, 181–191 (1968)Google Scholar
  40. 40.
    A problem of Schinzel on lattice points. Acta Arith. 15, 199–203 (1969)Google Scholar
  41. 41.
    with H. Davenport: Approximation to real numbers by algebraic integers. Acta Arith. 15, 393–416 (1969)zbMATHMathSciNetGoogle Scholar
  42. 42.
    Disproof of some conjectures on Diophantine approximations. Stud. Sci. Math. Hung. 4, 137–144 (1969)Google Scholar
  43. 43.
    Irregularities of distribution. II. Trans. Am. Math. Soc. 136, 347–360 (1969)Google Scholar
  44. 44.
    Irregularities of distribution. III. Pac J. Math. 29, 225–234 (1969)Google Scholar
  45. 45.
    Irregularities of distribution. IV. Invent. Math. 7, 55–82 (1969)Google Scholar
  46. 46.
    Badly approximable systems of linear forms. J. Number Theory 1, 139–154 (1969)Google Scholar
  47. 47.
    with H. Davenport: Dirichlet’s theorem on diophantine approximation. II. Acta Arith. 16, 413–424 (1970)zbMATHMathSciNetGoogle Scholar
  48. 48.
    Irregularities of distribution. V. Proc. Am. Math. Soc. 25, 608–614 (1970)Google Scholar
  49. 49.
    Simultaneous approximation to algebraic numbers by rationals. Acta Math. 125, 189–201 (1970)Google Scholar
  50. 50.
    with A. Baker: Diophantine approximation and Hausdorff dimension. Proc. Lond. Math. Soc. III. Ser. 21, 1–11 (1970)zbMATHCrossRefGoogle Scholar
  51. 51.
    with H. Davenport: Supplement to a theorem on linear forms. In: Turán, P. (ed.) Number Theory. Colloq. Math. Soc. János Bolyai, vol. 2, pp. 15–25. North-Holland, Amsterdam (1970)Google Scholar
  52. 52.
    with H. Davenport: Dirichlet’s theorem on diophantine approximation. In: Teoria dei Numeri, Istituto Nazionale di Alta Matematica, Rome, 1968. Symp. Math., 4, pp. 113–132. Academic Press, London (1970)Google Scholar
  53. 53.
    T-numbers do exist. In: Teoria dei Numeri, Istituto Nazionale di Alta Matematica, Rome, 1968. Symp. Math., 4, pp. 3–26. Academic Press, London (1970)Google Scholar
  54. 54.
    Remark on my paper: “Disproof of some conjectures on diophantine approximations ”. Stud. Sci. Math. Hung. 5, 479 (1970)Google Scholar
  55. 55.
    Some recent progress in diophantine approximations. In: Actes du Congrès International des Mathématiciens (Nice, 1970), tome 1, pp. 497–503. Gauthier-Villars, Paris (1971)Google Scholar
  56. 56.
    Diophantine approximation and certain sequences of lattices. Acta Arith. 18, 195–178 (1971)Google Scholar
  57. 57.
    Linear forms with algebraic coefficients. I. J. Number Theory 3, 253–277 (1971)Google Scholar
  58. 58.
    Linearformen mit algebraischen Koeffizienten. II. Math. Ann. 191, 1–20 (1971)Google Scholar
  59. 59.
    Approximation to algebraic numbers. Enseign. Math. II. Ser. 17, 187–253 (1971)Google Scholar
  60. 60.
    Mahler’s T-numbers. In: 1969 Number Theory Institute-Proceedings of the 1969 Summer Institute on Number Theory-American Mathematical Society. Proc. Symp. Pure Math., vol. 20, pp. 275–286. American Mathematical Society, Providence, R.I. (1971)Google Scholar
  61. 61.
    Diophantine equations involving norm forms. Sem. Mod. Methods Number Theory, Inst. Stat. Math. Tokyo 5 (1971)Google Scholar
  62. 62.
    On a problem of Heilbronn. J. Lond. Math. Soc. II. Ser 4, 545–550 (1972)Google Scholar
  63. 63.
    Irregularities of distribution. VI. Compos. Math. 24, 63–74 (1972)Google Scholar
  64. 64.
    Norm form equations. Ann. Math. (2) 96, 526–551 (1972)Google Scholar
  65. 65.
    Volume, surface area and the number of integer points covered by a convex set. Arch. Math. (Basel) 23, 537–543 (1972)Google Scholar
  66. 66.
    Irregularities of distribution. VII. Acta Arith. 21, 45–50 (1972)Google Scholar
  67. 67.
    with G.H. Meisters: Translation-invariant linear forms on L 2 (G) for compact Abelian groups G. J. Funct. Anal. 11, 407–424 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
  68. 68.
    Approximation to Algebraic Numbers. Série des Conférences de l’Union Mathématique Internationale, 2; Monographies de l’Enseignement Mathématique, 19. L’Enseignement Mathématique, Université de Genève, Geneva (1972)Google Scholar
  69. 69.
    Simultaneous approximation to algebraic numbers by algebraic numbers in a given number field. In: Proceedings of the 1972 Number Theory Conference, Boulder, Colo., pp. 189–193. University of Colorado, Boulder, Colo. (1972)Google Scholar
  70. 70.
    Inequalities for resultants and for decomposable forms. In: Osgood, C.F. (ed.) Diophantine Approximation and Its Applications: Proceedings, pp. 235–253. Academic Press, New York (1973)Google Scholar
  71. 71.
    Zur Methode von Stepanov. In: Collection of articles dedicated to Carl Ludwig Siegel on the occasion of his seventy-fifth birthday, IV. Acta Arith. 24, 347–367 (1973)Google Scholar
  72. 72.
    A lower bound for the number of solutions of equations over finite fields. In: Collection of articles dedicated to K. Mahler on the occasion of his seventieth birthday. J. Number Theory 6, 448–480 (1974)Google Scholar
  73. 73.
    Irregularities of distribution. VIII. Trans. Am. Math. Soc. 198, 1–22 (1974)Google Scholar
  74. 74.
    Irregularities of distribution. IX. In: Collection of articles in memory of Jurii Vladimirovič Linnik. Acta Arith. 27, 385–396 (1975)Google Scholar
  75. 75.
    The measure of the intersection of rotates of a set on the circle. Proc. Am. Math. Soc. 48, 18–20 (1975)Google Scholar
  76. 76.
    Simultaneous approximation to algebraic numbers by elements of a number field. Monatsh. Math. 79, 55–66 (1975)Google Scholar
  77. 77.
    Rational approximation to solutions of linear differential equations with algebraic coefficients. Proc. Am. Math. Soc. 53, 285–289 (1975)Google Scholar
  78. 78.
    Applications of Thue’s method in various branches of number theory. In: Proceedings of the International Congress of Mathematicians-Canadian Mathematical Congress-International Mathemathical Union, Vancouver, B.C., 1974, vol. 1, pp. 177–185 (1975)Google Scholar
  79. 79.
    On Osgood’s effective Thue theorem for algebraic functions. Commun. Pure Appl. Math. 29, 749–763 (1976)Google Scholar
  80. 80.
    Two questions in Diophantine approximation. Monatsh. Math. 82, 237–245 (1976)Google Scholar
  81. 81.
    Equations over Finite Fields: an Elementary Approach. Lect. Notes Math., vol. 536. Springer, Berlin (1976)Google Scholar
  82. 82.
    Irregularities of distribution. X. In: Zassenhaus, H. (ed.) Number Theory and Algebra: Collected Papers Dedicated to Henry B. Mann, Arnold E. Ross, and Olga Taussky-Todd, pp. 311–329. Academic Press, New York (1977)Google Scholar
  83. 83.
    Small Fractional Parts of Polynomials. Regional Conference Series in Mathematics, 32. American Mathematical Society, Providence, R.I. (1977)Google Scholar
  84. 84.
    On the distribution modulo 1 of the sequence αn 2 + β n. Can. J. Math. 29, 819–826 (1977)Google Scholar
  85. 85.
    Diophantine approximation in power series fields. Acta Arith. 32, 275–296 (1977)Google Scholar
  86. 86.
    Lectures on Irregularities of Distribution: Notes Taken by T N. Shorey. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 56. Tata Institute of Fundamental Research, Bombay (1977)Google Scholar
  87. 87.
    Thue’s equation over function fields. J. Aust. Math. Soc. Sen A 25, 385–422 (1978)Google Scholar
  88. 88.
    Small zeros of additive forms in many variables. Trans. Am. Math. Soc. 248, 121–133 (1979)Google Scholar
  89. 89.
    Contributions to Diophantine approximation in fields of series. Monatsh. Math. 87, 145–165 (1979)Google Scholar
  90. 90.
    Small zeros of additive forms in many variables. II. Acta Math. 143, 219–232 (1979)Google Scholar
  91. 91.
    with Y. Wang: A note on a transference theorem of linear forms. Sci. Sin. 22, 276–280 (1979)zbMATHGoogle Scholar
  92. 92.
    Polynomial solutions of F(x, y) = z n. In: Ribenboim, P. (ed.) Proceedings of the Queen’s Number Theory Conference, 1979. Queens Pap. Pure Appl. Math., 54, pp. 33–65. Queen’s University, Kingston, Ont. (1980)Google Scholar
  93. 93.
    Diophantine inequalities for forms of odd degree. Adv. Math. 38 (1980), 128–151Google Scholar
  94. 94.
    Simultaneous p-adic zeros of quadratic forms. Monatsh. Math. 90, 45–65 (1980)Google Scholar
  95. 95.
    with A. Schinzel and H.P. Schlickewei: Small solutions of quadratic congruences and small fractional parts of quadratic forms. Acta Arith. 37, 241–248 (1980)zbMATHMathSciNetGoogle Scholar
  96. 96.
    Diophantine Approximation. Lect. Notes Math., vol. 785. Springer, Berlin (1980)Google Scholar
  97. 97.
    with R.C. Baker: Diophantine problems in variables restricted to the values 0 and 1. J. Number Theory 12, 460–486 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  98. 98.
    with R.C. Baker: Addendum: “Diophantine problems in variables restricted to the values 0 and 1 ”. J. Number Theory 13, 270 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  99. 99.
    Simultaneous rational zeros of quadratic forms. In: Seminar on Number Theory, Paris 1980–81. Prog. Math., vol. 22, pp. 281–307. Birkhäuser, Boston (1982)Google Scholar
  100. 100.
    On cubic polynomials. I. Hua’s estimate of exponential sums. Monatsh. Math. 93, 63–74 (1982)Google Scholar
  101. 101.
    On cubic polynomials. II. Multiple exponential sums. Monatsh. Math. 93, 141–168 (1982)Google Scholar
  102. 102.
    On cubic polynomials. III. Systems of p-adic equations. Monatsh. Math. 93, 211–223 (1982)Google Scholar
  103. 103.
    On cubic polynomials IV. Systems of rational equations. Monatsh. Math. 93, 329–348 (1982)Google Scholar
  104. 104.
    The joint distribution of the digits of certain integers-tuples. In: Erdős, P., Alpár, L., Halász, G., Sarözy, A. (eds.) Studies in Pure Mathematics: to the Memory of Paul Turán, pp. 605–622. Birkhäuser, Basel (1983)Google Scholar
  105. 105.
    with D.B. Leep: Systems of homogeneous equations. Invent. Math. 71, 539–549 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  106. 106.
    The density of integer points on homogeneous varieties. In: Seminar on Number Theory, Paris 1981–82. Prog. Math., vol. 38, pp. 283–286. Birkhäuser, Boston (1983)Google Scholar
  107. 107.
    Open problems in Diophantine approximation. In: Bertrand, D., Waldschmidt, M. (eds.) Approximations diophantiennes et nombres transcendants: colloque de Luminy, 1982. Prog. Math., vol. 31, pp. 271–287. Birkhäuser, Boston (1983)Google Scholar
  108. 108.
    Diophantine approximation properties of certain infinite sets. Trans. Am. Math. Soc. 278, 635–645 (1983)Google Scholar
  109. 109.
    Analytic methods for congruences, diophantine equations and approximations. In: Proceedings of the International Congress of Mathematicians, Warsaw, 1983, vol. 1, pp. 515–524. PWN, Warsaw (1984)Google Scholar
  110. 110.
    The solubility of certain p-adic equations. J. Number Theory 19, 63–80 (1984)Google Scholar
  111. 111.
    Bounds for exponential sums. Acta Arith. 44, 281–297 (1984)Google Scholar
  112. 112.
    Analytische Methoden für Diophantische Gleichungen: einführende Vorlesungen. DMV Seminar, vol. 5. Birkhäuser, Basel (1984)Google Scholar
  113. 113.
    Integer points on curves and surfaces. Monatsh. Math. 99, 45–72 (1985)Google Scholar
  114. 114.
    Small solutions of congruences in a large number of variables. Can. Math. Bull 28, 295–305 (1985)Google Scholar
  115. 115.
    Small zeros of quadratic forms. Trans. Am. Math. Soc. 291, 87–102 (1985)Google Scholar
  116. 116.
    The density of integer points on homogeneous varieties. Acta Math. 154, 243–296 (1985)Google Scholar
  117. 117.
    Small solutions of congruences with prime modulus. In: Loxton, J.H., Van der Poorten, A.J. (eds.) Diophantine Analysis: Proceedings of the Number Theory Section of the 1985 Australian Mathematical Society Convention (Kensington, N.S.W.). Lond. Math. Soc. Lect. Note Ser., 109, pp. 37–66. Cambridge University Press, Cambridge (1986)Google Scholar
  118. 118.
    Partitions of triangles into convex sets. Österr. Akad. Wiss. Math. Naturwiss. Kl. Sitzungsber. II 195, 167–169 (1986)Google Scholar
  119. 119.
    Integer points on hypersurfaces. Monatsh. Math. 102, 27–58 (1986)Google Scholar
  120. 120.
    Thue equations with few coefficients. Trans. Am. Math. Soc. 303, 241–255 (1987)Google Scholar
  121. 121.
    with E. Bombieri: On Thue’s equation. Invent. Math. 88, 69–81 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  122. 122.
    with A. Florian: Zerlegung von Dreiecken in Dreiecke mit Nebenbedingung. Geom. Dedicata 24, 363–368 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  123. 123.
    with J. Mueller: Trinomial Thue equations and inequalities. J. Reine Angew. Math. 379, 76–99 (1987)zbMATHMathSciNetGoogle Scholar
  124. 124.
    with H.P. Schlickewei: Quadratic geometry of numbers. Trans. Am. Math. Soc. 301, 679–690 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  125. 125.
    The number of solutions of Thue equations. In: Baker, A. (ed.) New Advances in Transcendence Theory, pp. 337–346. Cambridge University Press, Cambridge (1988)Google Scholar
  126. 126.
    with H.P. Schlickewei: Quadratic forms which have only large zeros. Monatsh. Math. 105, 295–311 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  127. 127.
    with J. Mueller: Thue’s equation and a conjecture of Siegel. Acta Math. 160, 207–247 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  128. 128.
    with J. Mueller: On the number of good rational approximations to algebraic numbers. Proc. Am. Math. Soc. 106, 859–866 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  129. 129.
    with H.P. Schlickewei: Isotrope Unterräume rationaler quadratischer Formen. Math. Z. 201, 191–208 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  130. 130.
    with E. Bombieri: Correction to: “On Thue’s equation ” [Invent. Math. 88 (1987), no. 1, 69-81, MR 88d: 11026]. Invent. Math. 97, 445 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  131. 131.
    The subspace theorem in Diophantine approximations. Compos. Math. 69, 121–173 (1989)Google Scholar
  132. 132.
    The number of solutions of norm form equations. Trans. Am. Math. Soc. 317, 197–227 (1990)Google Scholar
  133. 133.
    A remark on the heights of subspaces. In: Baker, A., Bollobaś, B., Hajnal, A. (eds.) A Tribute to Paul Erdos, pp. 359–360. Cambridge University Press, Cambridge (1990)Google Scholar
  134. 134.
    The number of solutions of norm form equations. In: Győry, K., Halasz (eds.) Number Theory, vol. 2. Colloq. Math. Soc. János Bolyai, vol. 51, pp. 965–979. North-Holland, Amsterdam (1990)Google Scholar
  135. 135.
    Eisenstein’s theorem on power series expansions of algebraic functions. Acta Arith. 56, 161–179 (1990)Google Scholar
  136. 136.
    with H.P. Schlickewei: Bounds for zeros of quadratic forms. In: Győry, K., Halaśz (eds.) Number Theory, vol. 2. Colloq. Math. Soc. János Bolyai, vol. 51, pp. 951–964. North-Holland, Amsterdam (1990)Google Scholar
  137. 137.
    Diophantine Approximations and Diophantine Equations. Lect. Notes Math., vol. 1467. Springer, Berlin (1991)Google Scholar
  138. 138.
    On the number of good simultaneous approximations to algebraic numbers. In: Gong, S. (ed.) International Symposium in Memory of Hua Loo Keng, vol. I, pp. 249–264. Springer, Berlin (1991)Google Scholar
  139. 139.
    Construction and estimation of bases in function fields. J. Number Theory 39, 181–224 (1991)Google Scholar
  140. 140.
    Integer points on curves of genus 1. Compos. Math. 81, 33–59 (1992)Google Scholar
  141. 141.
    with J. Mueller: On the Newton polygon. Monatsh. Math. 113, 33–50 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  142. 142.
    with H.P. Schlickewei: On polynomial-exponential equations. Math. Ann. 296, 339–361 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  143. 143.
    Vojta’s refinement of the subspace theorem. Trans. Am. Math. Soc. 340, 705–731 (1993)Google Scholar
  144. 144.
    with H.P. Schlickewei: Equations au l n = bu k m satisfied by members of recurrence sequences. Proc. Am. Math. Soc. 118, 1043–1051 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  145. 145.
    Northcott’s theorem on heights. I. A general estimate. Monatsh. Math. 115, 169–181 (1993)Google Scholar
  146. 146.
    with H.P. Schlickewei: Linear equations in members of recurrence sequences. Ann. Sc. Norm. Super. Pisa Cl. Sci. IV. Ser. 20, 219–246 (1993)zbMATHMathSciNetGoogle Scholar
  147. 147.
    Bemerkungen zur Polynomdiskrepanz. Österr. Akad. Wiss. Math. Naturwiss. Kl. Sitzungsber. II 202, 173–177 (1993)Google Scholar
  148. 148.
    Equations α x = R(x, y). J. Number Theory 47, 348–358 (1994)Google Scholar
  149. 149.
    Approximation to orthogonal bases in ℝ.n by orthogonal bases with integer coordinates. Appendix to: “Approximation of viscosity solutions of elliptic partial differential equations on minimal grids ” [Numer. Math. 72 (1995), 73-92] by M. Kocan. Numer. Math. 72, 117–122 (1995)Google Scholar
  150. 150.
    Northcott’s theorem on heights. II. The quadratic case. Acta Arith. 70, 343–375 (1995)Google Scholar
  151. 151.
    with J. Mueller: The generalized Thue inequality. Compos. Math. 96, 331–344 (1995)zbMATHMathSciNetGoogle Scholar
  152. 152.
    Number fields of given degree and bounded discriminant. Astérisque 228, 189–195 (1995)Google Scholar
  153. 153.
    with H.P. Schlickewei: The intersection of recurrence sequences. Acta Arith. 72, 1–44 (1995)zbMATHMathSciNetGoogle Scholar
  154. 154.
    The number of exceptional approximations in Roth’s theorem. J. Aust. Math. Soc. Ser. A 59, 375–383 (1995)Google Scholar
  155. 155.
    Heights of algebraic points lying on curves or hypersurfaces. Proc. Am. Math. Soc. 124, 3003–3013 (1996)Google Scholar
  156. 156.
    Heights of points on subvarieties of \( \mathbb{G}_m^n \). In: Number Theory: Séminaire de théorie des nombres de Paris 1993–1994. Lond. Math. Soc. Lect. Note Ser., 235, pp. 157–187. Cambridge University Press, Cambridge (1996)Google Scholar
  157. 157.
    with CL. Stewart: Congruences, trees, and p-adic integers. Trans. Am. Math. Soc. 349, 605–639 (1997)zbMATHCrossRefGoogle Scholar
  158. 158.
    The distribution of sublattices of ℤm. Monatsh. Math. 125, 37–81 (1998)Google Scholar
  159. 159.
    Heights of points on subvarieties of Gn m. In: Murty, V.K., Waldschmidt. M. (eds.) Number Theory: Ramanujan Mathematical Society, January 3-6, 1996, Tiruchirapalli, India. Contemp. Math., 210, pp. 97–99. American Mathematical Society, Providence, R.I. (1998)Google Scholar
  160. 160.
    with H.P. Schlickewei and M. Waldschmidt: Zeros of linear recurrence sequences. Manuscr. Math. 98, 225–241 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  161. 161.
    Heights of algebraic points. In: Yildirim, C.Y., Stepanov, S.A. (eds.) Number Theory and Its Applications: Proceedings of a Summer School at Bilkent University. Lect. Notes Pure Appl. Math., vol. 204, pp. 185–225. Dekker, New York (1999)Google Scholar
  162. 162.
    The zero multiplicity of linear recurrence sequences. Acta Math. 182, 243–282 (1999)Google Scholar
  163. 163.
    Solution trees of polynomial congruences modulo prime powers. In: Győry, K., Iwaniec, H., Urbanowicz, J. (eds.) Number Theory in Progress: Proceedings of the International Conference on Number Theory, in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997, vol. 1, pp. 451–471. de Gruyter, Berlin (1999)Google Scholar
  164. 164.
    with H.P. Schlickewei: The number of solutions of polynomial-exponential equations. Compos. Math. 120, 193–225 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  165. 165.
    Zeros of linear recurrence sequences. Publ. Math. (Debrecen) 56, 609–630 (2000)Google Scholar
  166. 166.
    with S. Caulk: Simultaneous approximation in positive characteristic. Monatsh. Math. 131, 15–28 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  167. 167.
    On continued fractions and Diophantine approximation in power series fields. Acta Arith. 95, 139–166 (2000)Google Scholar
  168. 168.
    with B. Brindza and Á.Pintér: Multiplicities of binary recurrences. Can. Math. Bull. 44, 19–21 (2001)zbMATHGoogle Scholar
  169. 169.
    with A. Schinzel: Comparison of L 1-and L -norms of squares of polynomials. Acta Arith. 104, 283–296 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  170. 170.
    with J.-H. Evertse and H.P. Schlickewei: Linear equations in variables which lie in a multiplicative group. Ann. Math. (2) 155, 807–836 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  171. 171.
    with D. Evans and A.J. Jones: Asymptotic moments of near-neighbour distance distributions. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci 458, 2839–2849 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  172. 172.
    Complementary sets of finite sets. Monatsh. Math. 138, 61–71 (2003)Google Scholar
  173. 173.
    Linear recurrence sequences. In: Amoroso, F., Zannier, U. (eds.) Diophantine Approximation: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 28-July 6, 2000. Lect. Notes Math., vol. 1819, pp. 171–247. Springer, Berlin (2003)Google Scholar
  174. 174.
    Equations over Finite Fields: an Elementary Approach, 2nd edn. Kendrick Press, Heber City, Utah (2004)Google Scholar
  175. 175.
    Diophantine equations E(x) = P(x) with E exponential, P polynomial. Acta Arith. 113, 351–362 (2004)Google Scholar
  176. 176.
    Rationality of exponential functions at integer arguments. J. Number Theory 106, 285–298 (2004)Google Scholar
  177. 177.
    with I. Aliev and A. Schinzel: On vectors whose span contains a given linear subspace. Monatsh. Math. 144, 177–191 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  178. 178.
    with A. Schinzel: The mathematical work of Eduard Wirsing. Funct. Approximatio Comment. Math. 35, 7–18 (2006)zbMATHMathSciNetGoogle Scholar
  179. 179.
    Mahler and Koksma classification of points in ∝.n and ℂn. Funct. Approximatio Comment. Math. 35, 307–319 (2006)Google Scholar
  180. 180.
    Diophantine approximation by algebraic hypersurfaces and varieties. Trans. Am. Math. Soc. 359, 2221–2241 (2007)Google Scholar

Additional cited references

  1. [Ba]
    Baker, R.C: Weyl sums and Diophantine approximation. J. Lond. Math. Soc. II. Ser. 25, 25–34 (1982)zbMATHCrossRefGoogle Scholar
  2. [Be]
    Beck, J.: Sums of distances between points on a sphere-an application of the theory of irregularities of distributions to discrete geometry. Mathematika 31, 33–41 (1984)zbMATHMathSciNetGoogle Scholar
  3. [Bi]
    Birch, B.J.: Homogeneous forms of odd degree in a large number of variables. Mathematika 4, 102–105 (1957)zbMATHMathSciNetGoogle Scholar
  4. [Bo]
    Bombieri, E.: Counting points on curves over finite fields (d’après S.A. Stepanov). In: Séminaire Bourbaki, 1972/73, Exposes 418-435. Lect. Notes Math., vol. 383, pp. 234–241. Springer, Berlin (1974)CrossRefGoogle Scholar
  5. [BZ]
    Bombieri, E., Zannier, U.: Algebraic points on subvarieties of Gn m. Int. Math. Res. Not. 7, 333–347 (1995)CrossRefMathSciNetGoogle Scholar
  6. [C1]
    Cassels, J.W.S.: Bounds for the least solutions of homogeneous quadratic equations. Proc. Camb. Philos. Soc. 51, 262–264 (1955)CrossRefMathSciNetGoogle Scholar
  7. [C2]
    Cassels, J.W.S.: An Introduction to the Geometry of Numbers. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Bd. 99. Springer, Berlin (1959)zbMATHGoogle Scholar
  8. [Da]
    Danicic, I.: An extension of a theorem of Heilbronn. Mathematika 5, 249–256 (1958)MathSciNetCrossRefGoogle Scholar
  9. [DP]
    David, S., Philippon, P.: Minorations des hauteurs normalisées des sou-variétés des tores. Ann. Sc. Norm. Super. Pisa Cl. Sci IV. Ser. 28, 489–543 (1999)zbMATHMathSciNetGoogle Scholar
  10. [ES]
    Evertse, J.-H., Schlickewei, H.P.: A quantitative version of the absolute subspace theorem. J. Reine Angew. Math. 548, 21–127 (2002)zbMATHMathSciNetGoogle Scholar
  11. [He]
    Heilbronn, H.A.: On the distribution of the sequence n 2 θ(mod1). Q. J. Math. Oxf. Ser. 19, 249–256 (1948)CrossRefMathSciNetGoogle Scholar
  12. [H1]
    Hlawka, E.: Zur Geometrie der Zahlen. Math. Z. 42, 285–312 (1943)CrossRefMathSciNetGoogle Scholar
  13. [Ma]
    Mahler, K.: Zur Approximation der Exponentialfunktion und des Logarithmus I. J. Reine Angew. Math. 166, 118–136 (1932)Google Scholar
  14. [Pi]
    Pitman, J.: Cubic inequalities. J. Lond. Math. Soc. 43, 119–126 (1968)zbMATHCrossRefMathSciNetGoogle Scholar
  15. [R1]
    Roth, K.F.: On irregularities of distribution. Mathematika 1, 73–79 (1954)zbMATHMathSciNetGoogle Scholar
  16. [R2]
    Roth, K.F.: Rational approximations to algebraic numbers. Mathematika 2, 1–20 (1955)MathSciNetCrossRefGoogle Scholar
  17. [St]
    Stepanov, S.A.: An elementary proof of the Hasse-Weil theorem for hyperelliptic curves. J. Number Theory 4, 118–143 (1972)zbMATHCrossRefGoogle Scholar
  18. [Th]
    Thue, A.: Om en generel i store hele tal uløsbar ligning. Christiania Vidensk. Selsk. Skr. I Mat. Nat. Kl. 7 (1908)Google Scholar
  19. [W1]
    Wirsing, E.: Approximation mit algebraischen Zahlen beschränkten Grades. J. Reine Angew. Math. 206, 67–77 (1961)zbMATHMathSciNetGoogle Scholar
  20. [W2]
    Wirsing, E.: On approximation of algebraic numbers by algebraic numbers of bounded degree. In: 1969 Number Theory Institute-Proceedings of the 1969 Summer Institute on Number Theory-American Mathematical Society. Proc. Symp. Pure Math., 20, pp. 213–247. American Mathematical Society, Providence, R.I. (1971)Google Scholar
  21. [Zh]
    Zhang, S.: Positive line bundles on arithmetic surfaces. Ann. Math. 136, 569–587 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Hans Peter Schlickewei
    • 1
  1. 1.Fachbereich Mathematik und InformatikPhilipps-Universität MarburgMarburgGermany

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