Advertisement

The Heritage

  • Władysław Narkiewicz
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

This chapter brings a short overview of the development of number theory in the 19th century, pointing out the main achievements of that period.

Keywords

Number Theory Algebraic Number Diophantine Equation Riemann Hypothesis Transcendental Entire Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 42.
    Alasia, C.: Ernest Cesàro. 1859–1916. Enseign. Math. 9, 5–24 (1907) Google Scholar
  2. 43.
    Albert, A.A.: Leonard Eugene Dickson. Bull. Am. Math. Soc. 61, 331–345 (1955) MATHCrossRefGoogle Scholar
  3. 46.
    Aleksandrov, P.S. (ed.): Hilbert’s Problems. Nauka, Moscow (1969) (in Russian) [German translation: Harri Deutsch, Frankfurt 1998] Google Scholar
  4. 84.
    Andrews, G.E., Askey, R.A., Berndt, B.C., Ramanathan, K.G., Rankin, R.A. (eds.): Ramanujan Revisited (Proceedings of the Centenary Conference). Academic Press, San Diego (1988) MATHGoogle Scholar
  5. 198.
    Bachmann, P.: Zahlentheorie, I–V. Leipzig, 1872–1905 Google Scholar
  6. 200.
    Bachmann, P.: Über Gauß’ zahlentheoretische Arbeiten. Nachr. Ges. Wiss. Göttingen, 1911, 455–508 Google Scholar
  7. 456.
    Berndt, B.C., Rankin, R.A. (eds.): Ramanujan: Letters and Commentary. Am. Math. Soc./Lond. Math. Soc., Providence/London (1995) MATHGoogle Scholar
  8. 457.
    Berndt, B.C., Rankin, R.A. (eds.): Ramanujan: Essays and Surveys. Am. Math. Soc./Lond. Math. Soc., Providence/London (2001) MATHGoogle Scholar
  9. 744.
    Browder, F. (ed.): Mathematical Developments Arising from Hilbert Problems, I, II. Am. Math. Soc., Providence (1976) Google Scholar
  10. 852.
    Burckhardt, J.J., Fellman, E.A., Habicht, W. (eds.): Leonhard Euler 1707–1783: Beiträge zu Leben und Werk. Birkhäuser, Basel (1983) MATHGoogle Scholar
  11. 865.
    Burkill, J.C.: John Edensor Littlewood. Bull. Lond. Math. Soc. 11, 59–103 (1979) MathSciNetMATHCrossRefGoogle Scholar
  12. 878.
    Cahen, E.: Sur la fonction ζ(s) de Riemann et sur des fonctions analogues. Ann. Sci. Éc. Norm. Super. 11, 75–164 (1894) MathSciNetGoogle Scholar
  13. 879.
    Cahen, E.: Éléments de la théorie des nombres. Gauthier-Villars, Paris (1900) MATHGoogle Scholar
  14. 969.
    Čebyšev, P.L.: The Theory of Congruences, St. Petersburg, 1849 (in Russian) [2nd ed. 1879, 3rd ed. 1901; [973], vol. 1, pp. 10–172. German translation: Theorie der Congruenzen, Berlin, 1889, 1902; Italian translation: Teoria delle congruenze, Rome 1895] Google Scholar
  15. 970.
    Čebyšev, P.L.: Mémoire sur nombres premiers. Mémoires des savants étrangers de l’Acad. Sci. St. Pétersbourg 7, 17–33 (1850) [J. math. pures appl., 17, 366–390 (1852); Oeuvres, vol. 1, pp. 49–70, S. Pétersbourg 1899, reprint: Chelsea, 1962; [973], vol. 1, pp. 191–207 (in Russian)] Google Scholar
  16. 1051.
    Chevalley, C.: Emil Artin (1898–1962). Bull. Soc. Math. Fr. 92, 1–10 (1964) MathSciNetMATHGoogle Scholar
  17. 1259.
    Courant, R.: Felix Klein. Jahresber. Dtsch. Math.-Ver. 34, 197–213 (1926) MATHGoogle Scholar
  18. 1419.
    Decaillot-Laulagnet, A.-M.: Édouard Lucas (1842–1891): le parcours original d’un scientifique français dans la deuxième moitié du XIXe siècle. Thése, Univ. Paris V (1999) Google Scholar
  19. 1422.
    Dedekind, R.: Über die Anzahl von Idealklassen in reinen kubischen Zahlkörpern. J. Reine Angew. Math. 121, 40–123 (1900) [[1423], vol. 2, pp. 148–233] CrossRefGoogle Scholar
  20. 1423.
    Dedekind, R.: Gesammelte mathematische Werke. Vieweg, Wiesbaden (1931). [Reprint: Chelsea, 1968] Google Scholar
  21. 1533.
    Dick, A.: Franz Mertens, 1840–1927. Forschungszentrum Graz, Graz (1981) MATHGoogle Scholar
  22. 1545.
    Dickson, L.E.: History of the Theory of Numbers. Carnegie Institution of Washington, Washington (1919) [Reprints: Chelsea, 1952, 1966] MATHGoogle Scholar
  23. 1569.
    Dickson, L.E., Mitchell, H.H., Vandiver, H.S., Wahlin, G.E.: Algebraic Numbers, Report of the Committee on Algebraic Numbers. National Research Council, Washington (1923) MATHGoogle Scholar
  24. 1580.
    Dipert, R.R.: The life and logical contribution of O.H. Mitchell, Peirce’s gifted student. Trans. C.S. Peirce’s Soc. 30, 515–542 (1994) Google Scholar
  25. 1584.
    Dirichlet, P.G.L.: Beweis eines Satzes ueber die arithmetische Progression. Ber. Verhandl. Kgl. Preuß. Akad. Wiss., 1837, 108–110 [[1593], pp. 307–312] Google Scholar
  26. 1585.
    Dirichlet, P.G.L.: Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält. Abhandl. Kgl. Preuß. Akad. Wiss., 1837, 45–81 [[1593], pp. 313–342; French translation: J. Math. Pures Appl. 4, 393–422 (1839)] Google Scholar
  27. 1586.
    Dirichlet, P.G.L.: Sur l’usage des séries infinies dans la théorie des nombres. J. Reine Angew. Math. 18, 259–274 (1838) [[1593], pp. 357–374] MATHCrossRefGoogle Scholar
  28. 1587.
    Dirichlet, P.G.L.: Recherches sur diverses applications de l’analyse infinitésimale à la théorie des nombres. J. Reine Angew. Math. 19, 324–369 (1839), 21, 1–12, 134–155 (1840) [[1593], pp. 411–496] Google Scholar
  29. 1592.
    Dirichlet, P.G.L.: Vorlesungen über Zahlentheorie. Springer, Berlin (1863), 2nd ed. 1871, 3rd ed. 1879, 4th ed. 1894 [Reprint: Chelsea, 1968; English translation: Am. Math. Soc., 1999] Google Scholar
  30. 1593.
    Dirichlet, P.G.L.: Werke, vol. 1, Springer, Berlin (1889) [Reprint: Chelsea, 1969] MATHGoogle Scholar
  31. 1594.
    Dirichlet, P.G.L.: Werke, vol. 2, Springer, Berlin (1897) [Reprint: Chelsea, 1969] MATHGoogle Scholar
  32. 1653.
    Dunnington, G.W.: Carl Friedrich Gauss. Titan of Science. Exposition Press, New York (1955) [Reprint: Math. Assoc. of America, 2004] MATHGoogle Scholar
  33. 1691.
    Edwards, H.M.: Riemann’s Zeta Function. Academic Press, San Diego (1974) [Reprint: Dover 2001] MATHGoogle Scholar
  34. 1909.
    Euler, L., Goldbach, C.: Briefwechsel 1729–1764. Akademie Verlag, Berlin (1965) Google Scholar
  35. 1982.
    Feldman, N.I.: The Seventh Problem of Hilbert. Moscow State University Press, Moscow (1982) (in Russian) Google Scholar
  36. 1986.
    Fellman, E.A.: Leonhard Euler. Rowohlt, Hamburg (1995). [English translation: Birkhäuser, 2007] Google Scholar
  37. 1996.
    Ferrers, N.M.: Series for \(\frac{\pi}{\sqrt{7}}\), \(\frac{\pi}{\sqrt{1}1}\), \(\frac{\pi}{\sqrt{1}9}\). Messenger Math. 31, 92–94 (1901/1902) Google Scholar
  38. 1998.
    Fields, J.C.: A simple statement of proof of reciprocal theorem. Am. J. Math. 13, 189–190 (1891) MathSciNetCrossRefGoogle Scholar
  39. 2042.
    Forsyth, A.R.: James Whitbread Lee Glaisher. J. Lond. Math. Soc. 4, 101–112 (1929) MATHCrossRefGoogle Scholar
  40. 2071.
    Frei, G.: Helmut Hasse (1898–1979). Expo. Math. 3, 55–69 (1985) MathSciNetMATHGoogle Scholar
  41. 2072.
    Frei, G.: Heinrich Weber and the emergence of class field theory. In: The History of Modern Mathematics, vol. 1, pp. 425–450. Academic Press, San Diego (1989) Google Scholar
  42. 2168.
    Fuss, P.H.: Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIéme siécle. St. Pétersbourg (1843) [Reprint: Johnson Reprint Co. 1968] Google Scholar
  43. 2208.
    Gauss, C.F.: Disquisitiones Arithmeticae. Fleischer, Leipzig (1801) [[2214], vol. 1, pp. 1–474; German translation: Untersuchungen über höhere Arithmetik, Springer, 1889; reprint: Chelsea, 1965; English translation: Yale, 1966; Springer, 1986] Google Scholar
  44. 2211.
    Gauss, C.F.: Theoria residuorum biquadraticorum. Comm. Soc. Reg. Sci. Gottingensis, 6 (1828); 7 (1832) [[2214], vol. 2, pp. 65–92, 93–148] Google Scholar
  45. 2239.
    Gimbel, S., Jaroma, J.H.: Sylvester: ushering in the modern era of research on odd perfect numbers. Integers 3(#A16), 1–26 (2003) MathSciNetGoogle Scholar
  46. 2242.
    Glaisher, J.W.L.: Classes of recurring formulae involving Bernoullian numbers. Messenger Math. 28, 36–79 (1898/1899) Google Scholar
  47. 2243.
    Glaisher, J.W.L.: On a set of coefficients analogous to the Eulerian numbers. Proc. Lond. Math. Soc. 31, 216–235 (1899) MATHCrossRefGoogle Scholar
  48. 2244.
    Glaisher, J.W.L.: A congruence theorem relating to Eulerian numbers and other coefficients. Proc. Lond. Math. Soc. 32, 171–198 (1900) MATHCrossRefGoogle Scholar
  49. 2245.
    Glaisher, J.W.L.: A series for \(\frac{\pi}{\sqrt{7}}\). Messenger Math. 31, 50–52 (1901/1902) Google Scholar
  50. 2246.
    Glaisher, J.W.L.: On series for \(\frac{\pi}{\sqrt{p}}\). Messenger Math. 31, 98–115 (1901/1902) Google Scholar
  51. 2247.
    Glaisher, J.W.L.: A general congruence theorem relating to the Bernoullian function. Proc. Lond. Math. Soc. 33, 27–56 (1901) MATHCrossRefGoogle Scholar
  52. 2349.
    Grodzenskiĭ, S.Ya.: Andreĭ Andreevič Markov. 1856–1922. Nauka, Moscow (1987) (in Russian) Google Scholar
  53. 2426.
    Hadamard, J.: Sur la distribution des zéros de la fonction ζ(s) et ses conséquences arithmétiques. Bull. Soc. Math. Fr. 24, 199–200 (1896) [Selecta, pp. 111–132, Gauthier-Villars, Paris, 1935] MathSciNetMATHGoogle Scholar
  54. 2504.
    Hardy, G.H.: A formula for the prime factors of any numbers. Messenger Math. 35, 145–146 (1905/1906) Google Scholar
  55. 2512.
    Hardy, G.H.: Srinivasa Ramanujan (1887–1920). Proc. Lond. Math. Soc. 19, xl–lviii (1921) [[5088], xxi–xxxvi] MATHCrossRefGoogle Scholar
  56. 2516.
    Hardy, G.H.: Ramanujan. Cambridge University Press, Cambridge (1940) Google Scholar
  57. 2518.
    Hardy, G.H., Heilbronn, H.: Edmund Landau. J. Lond. Math. Soc. 13, 302–310 (1938) [[3680], vol. 1, pp. 15–23; [2715], pp. 351–359] CrossRefGoogle Scholar
  58. 2603.
    Hasse, H.: Kurt Hensel zum Gedächtnis. J. Reine Angew. Math. 187, 1–13 (1949) MathSciNetMATHGoogle Scholar
  59. 2613.
    Hathaway, A.S.: A memoir in the theory of numbers. Am. J. Math. 9, 162–179 (1887) MathSciNetCrossRefGoogle Scholar
  60. 2749.
    Hensel, K.: Paul Bachmann und sein Lebenswerk. Jahresber. Dtsch. Math.-Ver. 36, 31–73 (1927) MATHGoogle Scholar
  61. 2782.
    Hilbert, D.: Ein neuer Beweis des Kronecker’schen Fundamentalsatzes über Abel’sche Zahlkörper. Nachr. Ges. Wiss. Göttingen, 1896, 29–39 Google Scholar
  62. 2783.
    Hilbert, D.: Die Theorie der algebraischer Zahlkörper. Jahresber. Dtsch. Math.-Ver. 4, 175–546 (1897) [[2792], 1, 63–363; English translation: The Theory of Algebraic Number Fields, Springer, 1998; French translation: Ann. Fac. Sci. Toulouse 1, 257–328 (1909); 2, 225–456 (1910)] Google Scholar
  63. 2785.
    Hilbert, D.: Ueber die Theorie der relativ-Abelschen Zahlkörper Nachr. Ges. Wiss. Göttingen, 1898, 377–399. Acta Math. 26, 1902, 99–132 [[2792], vol. 1, pp. 483–509] Google Scholar
  64. 2786.
    Hilbert, D.: Ueber die Theorie des relativ-quadratischen Zahlkörpers. Math. Ann. 51, 1–127 (1899) [[2792], vol. 1, pp. 370–482] MATHCrossRefGoogle Scholar
  65. 2788.
    Hilbert, D.: Mathematische Probleme, Arch. Math. 1, 44–63, 213–237 (1901). [[2792], vol. 3, pp. 290–329; English translation: Mathematical problems. Bull. Am. Math. Soc. 8, 437–479 (1901/1902); reprint, (N.S.), 37, 407–436 (2000)] Google Scholar
  66. 2790.
    Hilbert, D.: Herrmann Minkowski. Math. Ann. 68, 445–471 (1910) [[2792], vol. 3, pp. 339–364] MathSciNetMATHCrossRefGoogle Scholar
  67. 2791.
    Hilbert, D.: Adolf Hurwitz. Math. Ann. 83, 161–172 (1921) [[2792], vol. 3, pp. 370–377] MathSciNetMATHCrossRefGoogle Scholar
  68. 2835.
    Hlawka, E.: Carl Ludwig Siegel (31/12/1896–4/4/1981). J. Number Theory 20, 373–404 (1985) MathSciNetMATHCrossRefGoogle Scholar
  69. 2846.
    Hofreiter, N.: Nachruf auf Philipp Furtwängler. Monatshefte Math. Phys. 49, 219–227 (1940) MathSciNetMATHCrossRefGoogle Scholar
  70. 2849.
    Holzapfel, R.-P.: The Ball and some Hilbert Problems. Birkhäuser, Basel (1995) MATHGoogle Scholar
  71. 2852.
    Honda, K.: Teiji Takagi: a biography—on the 100th anniversary of his birth. Comment. Math. Univ. St. Pauli 24, 141–167 (1975/1976) MathSciNetGoogle Scholar
  72. 2942.
    Huber, A.: Philipp Furtwängler. Jahresber. Dtsch. Math.-Ver. 50, 167–178 (1940) MATHGoogle Scholar
  73. 3075.
    Jacobi, C.G.J.: Note sur la décomposition d’un nombre donné en quatre carrés. J. Reine Angew. Math. 3, 191 (1828) [[3082], vol. 1, pp. 245–247] CrossRefGoogle Scholar
  74. 3077.
    Jacobi, C.G.J.: Fundamenta nova theoriae functionum ellipticarum. Bornträger, Regiomonti (1829) [[3082], vol. 1, pp. 49–239] Google Scholar
  75. 3237.
    Kanigel, R.: The Man Who Knew Infinity. Charles Scribner’s Sons, New York (1991) MATHGoogle Scholar
  76. 3250.
    Kaplansky, I.: Hilbert’s Problems. University of Chicago Press, Chicago (1977) Google Scholar
  77. 3285.
    Kaufmann-Bühler, W.: Gauss. A Biographical Study. Springer, Berlin (1981) Google Scholar
  78. 3354.
    Klein, F.: Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, I. Springer, Berlin (1926) MATHGoogle Scholar
  79. 3355.
    Klein, F.: Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, II. Springer, Berlin (1927) Google Scholar
  80. 3403.
    Kneser, A.: Leopold Kronecker. Jahresber. Dtsch. Math.-Ver. 33, 210–228 (1925) MATHGoogle Scholar
  81. 3418.
    Knopp, K.: Edmund Landau. Jahresber. Dtsch. Math.-Ver. 54, 55–62 (1951) MathSciNetMATHGoogle Scholar
  82. 3433.
    von Koch, H.: Sur la distribution des nombres premiers. Acta Math. 24, 159–182 (1901) MathSciNetCrossRefGoogle Scholar
  83. 3438.
    Koenigsberger, L.: Carl Gustav Jacob Jacobi. Jahresber. Dtsch. Math.-Ver. 13, 405–435 (1904) Google Scholar
  84. 3439.
    Koenigsberger, L.: Carl Gustav Jacob Jacobi. Teubner, Leipzig (1904) Google Scholar
  85. 3489.
    Korobov, N.M., Nesterenko, Yu.V., Shidlovskii, A.B.: Naum Il’ič Feldman. Usp. Mat. Nauk 50(6), 157–162 (1995) (in Russian) MathSciNetGoogle Scholar
  86. 3524.
    Kronecker, L.: Über die algebraisch auflösbaren Gleichungen. Mon. Ber. Kgl. Preuß. Akad. Wiss., 1853, 365–374; 1856, 203–215. [[3532], vol. 4, pp. 1–11, 25–37] Google Scholar
  87. 3583.
    Kummer, E.E.: Collected Papers, vols. 1, 2, Springer, Berlin (1975) Google Scholar
  88. 3594.
    Kuzmin, R.O.: The life and scientific activity of Egor Ivanovič Zolotarev. Usp. Mat. Nauk 2(6), 21–51 (1947) (in Russian) MathSciNetGoogle Scholar
  89. 3624.
    Landau, E.: Über die Darstellung der Anzahl der Idealklassen eines algebraischen Körpers durch eine unendliche Reihe. J. Reine Angew. Math. 127, 167–174 (1904) [[3680], vol. 2, pp. 145–152] MATHCrossRefGoogle Scholar
  90. 3722.
    Laugwitz, D.: Bernhard Riemann 1826–1866. Wendepunkte in der Auffassung der Mathematik. Birkhäuser, Basel (1996) [English translation: Birkhäuser, 1999, reprint: 2008] MATHGoogle Scholar
  91. 3754.
    Lebesgue, V.A.: Exercises d’analyse numerique. Leiber et Faraguet, Paris (1859) Google Scholar
  92. 3755.
    Lebesgue, V.A.: Introduction à la théorie des nombres. Mallet-Bachelier, Paris (1862) Google Scholar
  93. 3767.
    Legendre, A.M.: Essai sur la théorie des nombres, Duprat, Paris (1798) [2nd ed. 1808, 3rd ed.: Théorie des nombres, Paris, 1830; German translation: Teubner, 1886, 1894] Google Scholar
  94. 3868.
    Lévy, P., Mandelbrojt, S., Malgrange, B., Malliavin, P.: La vie et l’oeuvre de Jacques Hadamard (1865–1963). L’Enseignement Mathematique Universite, Genéve (1967) MATHGoogle Scholar
  95. 4030.
    Lucas, É.: Théorie des Nombres. Gauthier-Villars, Paris (1891) [Reprint: Blanchard, Paris, 1961] MATHGoogle Scholar
  96. 4035.
    Lützen, J.: Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics. Springer, Berlin (1990) MATHGoogle Scholar
  97. 4107.
    Maillet, E.: Quelques extensions du théorème de Fermat sur les nombres polygones. J. Math. Pures Appl. 2, 363–380 (1896) Google Scholar
  98. 4108.
    Maillet, E.: Sur l’équation indéterminée \(ax^{\lambda ^{t}}+by^{\lambda^{t}}=cz^{\lambda^{t}}\). In: C.R. 26 Session Assoc. Française pour l’avancement des Sciences, Paris, vol. 2, pp. 156–168 (1898) Google Scholar
  99. 4221.
    Maz’ya, V., Shaposhnikova, T.: Jacques Hadamard, a Universal Mathematician. Am. Math. Soc., Providence (1998) MATHGoogle Scholar
  100. 4259.
    Mertens, F.: Über eine Eigenschaft der Riemannscher ζ-Funktion. SBer. Kais. Akad. Wissensch. Wien 107, 1429–1434 (1898) MATHGoogle Scholar
  101. 4321.
    Minkowski, H.: Ueber Geometrie der Zahlen. Jahresber. Dtsch. Math.-Ver. 1, 64–65 (1890/1891) [[4329], vol. 1, pp. 264–265] Google Scholar
  102. 4327.
    Minkowski, H.: Peter Gustav Lejeune Dirichlet und seine Bedeutung für die heutige Mathematik. Jahresber. Dtsch. Math.-Ver. 14, 149–163 (1905) [[4329], vol. 2, pp. 447–461] Google Scholar
  103. 4338.
    Mitchell, O.H.: On binomial congruences; comprising an extension of Fermat’s and Wilson’s theorems, and a theorem on which both are special cases. Am. J. Math. 3, 294–315 (1880) CrossRefGoogle Scholar
  104. 4339.
    Mitchell, O.H.: Some theorems in numbers. Am. J. Math. 4, 25–38 (1881) CrossRefGoogle Scholar
  105. 4345.
    Miyake, K.: Teiji Takagi, founder of the Japanese School of Modern Mathematics. Jpn. J. Math. 2, 151–164 (2007) MathSciNetMATHCrossRefGoogle Scholar
  106. 4542.
    Narkiewicz, W.: The Development of Prime Number Theory. Springer, Berlin (2000) MATHGoogle Scholar
  107. 4579.
    Neumann, O.: Two proofs of the Kronecker-Weber theorem “according to Kronecker, and Weber”. J. Reine Angew. Math. 323, 105–126 (1981) MathSciNetMATHCrossRefGoogle Scholar
  108. 4624.
    Noether, M.: Charles Hermite. Math. Ann. 55, 337–385 (1902) MathSciNetMATHCrossRefGoogle Scholar
  109. 4686.
    Opolka, H., Scharlau, W.: From Fermat to Minkowski. Springer, Berlin (1985) MATHGoogle Scholar
  110. 4711.
    Ožigova, E.P.: The development of number theory in Russia. Nauka, Leningrad (1972) (in Russian) Google Scholar
  111. 4714.
    Padé, H.: Sur la généralisation des fractions continues algébriques. J. Math. Pures Appl. 10, 291–329 (1894) Google Scholar
  112. 4748.
    Parshall, K.H.: James Joseph Sylvester. Jewish Mathematician in a Victorian World. Johns Hopkins University Press, Baltimore (2006) MATHGoogle Scholar
  113. 4775.
    Pépin, T.: Solution de l’équation X 4+35Y 4=Z 2. J. Math. Pures Appl. 1, 351–358 (1895) Google Scholar
  114. 4784.
    Perron, O.: Zur Theorie der Dirichletschen Reihen. J. Reine Angew. Math. 134, 95–143 (1908) MATHCrossRefGoogle Scholar
  115. 4849.
    Picard, É.: L’oeuvre scientifique de Charles Hermite. Ann. Sci. Éc. Norm. Super. 18, 9–34 (1901) MathSciNetGoogle Scholar
  116. 4850.
    Picard, É.: L’oeuvre de Henri Poincaré. Ann. Sci. Éc. Norm. Super. 30, 463–482 (1913) MathSciNetGoogle Scholar
  117. 4935.
    Poincaré, H.: Extension aux nombres premiers complexes des théorèmes de M. Tchebicheff. J. Math. Pures Appl. 8, 25–68 (1892) Google Scholar
  118. 4936.
    Poincaré, H.: Sur les propriétés arithmétiques des courbes algébriques. J. Math. Pures Appl. 7, 161–233 (1901) Google Scholar
  119. 4998.
    Posse, K.A.: A.N. Korkin. Mat. Sb. 27, 1–27 (1909) (in Russian) Google Scholar
  120. 5015.
    Prudnikov, V.E.: Pafnutiĭ Lvovič Čebyšev (1821–1894). Nauka, Moscow (1976) (in Russian) Google Scholar
  121. 5149.
    Reid, C.: Hilbert. Springer, Berlin (1970) [Reprint: Hilbert–Courant, Springer, 1986] MATHGoogle Scholar
  122. 5224.
    Riemann, B.: Ueber die Anzahl der Primzahlen unter einer gegebener Grösse. Monatsber. Kgl. Preuß. Akad. Wiss. Berlin, 1860, 671–680 [Gesammelte mathematische Werke, 3–47, Leipzig, 1876; Reprint: Dover 1953; Springer, Teubner, 1990; English translation: Kendrick Press, 2004; French translation: Blanchard, 1968] Google Scholar
  123. 5422.
    Schappacher, N.: On the history of Hilbert’s twelfth problem: a comedy of errors. In: Matériaux pour l’histoire des mathématiques au XXe siècle, Nice, 1996, pp. 243–273. Soc. Math. France, Paris (1998) Google Scholar
  124. 5533.
    Schnack, I. (ed.): Lebensbilder aus Hessen: Marburger Gelehrte in der ersten Hälfte des 20. Jahrhunderts. Elwert, Marburg (1977) Google Scholar
  125. 5543.
    Schneider, T.: Das Werk C.L. Siegels in der Zahlentheorie. Jahresber. Dtsch. Math.-Ver. 85, 147–157 (1983) MATHGoogle Scholar
  126. 5659.
    Serre, J.-P.: Smith, Minkowski et l’Académie des Sciences. Math. Gaz. 56, 3–9 (1993) MATHGoogle Scholar
  127. 5667.
    Ševelev, F.J.: A short summary of the scientific work of N.V. Bugaev. Istor.-Mat. Issled. 12, 525–558 (1959) (in Russian) MathSciNetGoogle Scholar
  128. 5831.
    Smith, H.J.S.: Report on the theory of numbers. Rep. British Association, 1859, 228–267; 1860, 120–169; 1861, 292–340; 1862, 503–526; 1863, 768–786; 1865, 322–375. [[5834], vol. 1, pp. 38–364] Google Scholar
  129. 5846.
    Sommer, J.: Vorlesungen über Zahlentheorie. Einführung in die Theorie der algebraischen Zahlkörper. Teubner, Leipzig (1907) Google Scholar
  130. 5940.
    Steuding, J.: Voronoïs contribution to modern number theory. Šiauliai Math. Semin. 2, 67–106 (2007) MathSciNetGoogle Scholar
  131. 5960.
    Stolz, O.: Leopold Gegenbauer. Monatshefte Math. Phys. 15, 3–10, 129–136 (1904) Google Scholar
  132. 6008.
    Sylvester, J.J.: On Tchebycheff’s theory of the totality of the prime numbers comprised within given limits. Am. J. Math. 4, 230–247 (1881) [[6014], vol. 3, pp. 230–247] MathSciNetCrossRefGoogle Scholar
  133. 6009.
    Sylvester, J.J.: A constructive theory of partitions, arranged in three acts, an interact and an exodion. Am. J. Math. 5, 251–330 (1882) [[6014], vol. 4, pp. 1–83] MathSciNetCrossRefGoogle Scholar
  134. 6015.
    Synge, J.L.: John Charles Fields. J. Lond. Math. Soc. 8, 153–160 (1933) CrossRefGoogle Scholar
  135. 6181.
    Titchmarsh, E.C.: Godfrey Harold Hardy. J. Lond. Math. Soc. 25, 82–101 (1950) MathSciNetGoogle Scholar
  136. 6263.
    de la Vallée-Poussin, C.J.: Recherches analytiques sur la théorie des nombres premiers. Ann. Soc. Sci. Bruxelles 20, 183–256, 281–397 (1896) Google Scholar
  137. 6370.
    Vaughan, R.C.: Hardy’s legacy to number theory. J. Aust. Math. Soc. A 65, 238–266 (1998) MathSciNetMATHCrossRefGoogle Scholar
  138. 6450.
    Vlăduţ, S.G.: Kronecker’s Jugendtraum and Modular Functions. Gordon & Breach, New York (1991) MATHGoogle Scholar
  139. 6477.
    Voss, A.: Heinrich Weber. Jahresber. Dtsch. Math.-Ver. 23, 431–444 (1914) Google Scholar
  140. 6599.
    Weber, H.: Theorie der Abelscher Zahlkörper. Acta Math. 8, 193–263 (1886) MathSciNetMATHCrossRefGoogle Scholar
  141. 6600.
    Weber, H.: Theorie der Abelscher Zahlkörper, II. Acta Math. 9, 105–130 (1887) MathSciNetCrossRefGoogle Scholar
  142. 6601.
    Weber, H.: Elliptische Funktionen und algebraische Zahlen. Vieweg, Braunschweig (1894) Google Scholar
  143. 6602.
    Weber, H.: Lehrbuch der Algebra. vols. I–III. Vieweg, Braunschweig (1894–1908) Google Scholar
  144. 6603.
    Weber, H.: Über Zahlengruppen in algebraischen Körpern. Math. Ann. 48, 433–437 (1897) MathSciNetMATHCrossRefGoogle Scholar
  145. 6604.
    Weber, H.: Über Zahlengruppen in algebraischen Körpern, II. Math. Ann. 49, 83–100 (1897) MathSciNetMATHCrossRefGoogle Scholar
  146. 6605.
    Weber, H.: Über Zahlengruppen in algebraischen Körpern, III. Math. Ann. 50, 1–26 (1898) MathSciNetMATHCrossRefGoogle Scholar
  147. 6638.
    Western, A.E.: Allan Joseph Cunningham. J. Lond. Math. Soc. 3, 317–318 (1928) MATHCrossRefGoogle Scholar
  148. 6663.
    Wiener, N.: Godfrey Harold Hardy (1877–1947). Bull. Am. Math. Soc. 55, 72–77 (1949) MathSciNetMATHCrossRefGoogle Scholar
  149. 6794.
    Young, W.H.: Adolf Hurwitz. Proc. Lond. Math. Soc. 20, xlviii–liv (1922) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Institute of MathematicsWrocław UniversityWrocławPoland

Personalised recommendations