Skip to main content
SpringerLink
Log in

Zahlentheorie

  • Chapter
Alte und neue ungelöste Probleme in der Zahlentheorie und Geometrie der Ebene

  • 283 Accesses

Zusammenfassung

Viele ungelöste Probleme der Mathematik sind berühmt (oder berüchtigt), das Eigenschaftswort „wohlbekannt“ wird jedoch mehr zur Charakterisierung von Problemen der Zahlentheorie als zur Beschreibung von Problemen anderer Gebiete verwendet. Der Grund hierfür ist, daß sich in der Zahlentheorie Probleme, die einfach klingen und bei denen nur die elementarsten Begriffe der Arithmetik auftreten, als außerordentlich schwierig erwiesen haben. Aufgrund der Berühmtheit gewisser ungelöster Probleme (man denke z.B. an die Fermatsche Vermutung oder die Frage nach der Existenz einer ungeraden vollkommenen Zahl) tauchen regelmäßig Behauptungen auf, daß Lösungen gefunden worden seien. Alle diese Behauptungen haben sich jedoch als falsch herausgestellt, was den Bekanntheitsgrad dieser Probleme weiter erhöht. Zum Nimbus des Geheimnisvollen trägt auch die lange Geschichte einiger dieser Probleme bei: die Fermatsche Vermutung wurde vor vier Jahrhunderten formuliert, die Suche nach vollkommenen Zahlen begann bereits vor über zweitausend Jahren.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literaturhinweise

  1. L.M. Adleman and M.A. Huang, Recognizing primes in random polynomial time, Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, New York City, ACM Press, New York, 1987, S. 462–469. [§18]

    Google Scholar 

  2. L.V. Ahlfors, Complex Analysis, 2. Auflage, McGraw Hill, New York, 1966. [§17]

    MATH  Google Scholar 

  3. J.H.J. Almering, Rational quadrilaterals, Indagationes Mathematicae, 25 (1963) 192–199. [§14]

    MathSciNet  Google Scholar 

  4. E. Bach, Analytic Methods in the Analysis and Design of Number-Theoretic Algorithms, ACM Distinguished Dissertations, MIT Press, Cambridge, 1985. [§18]

    Google Scholar 

  5. A. Beck, M.N. Bleicher, and D.W. Crowe, Excursions into Mathematics, Worth, New York, 1969. [§15]

    Google Scholar 

  6. M.N. Bleicher, A new algorithm for the expansion of Egyptian fractions, Journal ofNumber Theory, 4 (1972) 342–382. [§15]

    MathSciNet  MATH  Google Scholar 

  7. R.P. Boas, The Skewes number, in Mathematical Plums, R. Honsberger, Hrsg., Dolciani Mathematical Expositions, No. 4, Mathematical Association of America, 1979. [§17]

    Google Scholar 

  8. W. Borho and H. Hoffmann, Breeding amicable numbers in abundance, Mathematics of Computation, 46 (1986) 281–293. [§16]

    MathSciNet  MATH  Google Scholar 

  9. R.P. Brent and G.L. Cohen, A new lower bound for odd perfect numbers, Mathematics of Computation, 53 (1989) 431–437. [§16]

    MathSciNet  MATH  Google Scholar 

  10. R.P. Brent, G.L. Cohen, and H.J.J. te Riele, An improved technique for lower bounds for odd perfect numbers, Australian National University Technical Report. [§16]

    Google Scholar 

  11. A. Bremner and R.K. Guy, A dozen difficult Diophantine dilemmas, American Mathematical Monthly, 95 (1988) 31–36. [§14]

    MathSciNet  MATH  Google Scholar 

  12. R. Breusch, Solution to Problem E4512, American Mathematical Monthly, 61 (1954) 200–201. [§15]

    MathSciNet  Google Scholar 

  13. J. Brillhart, D.H. Lehmer, J.L. Selfridge, B. Tuckerman, and S.S. Wagstaff, Jr., Factorizations of b n − 1, b = 2,3,5,6,7,10,11,12 up to high powers, second ed., Contemporary Mathematics, vol. 22, American Mathematical Society, Providence, 1988. [§18]

    Google Scholar 

  14. D. Burton, The History of Mathematics, An Introduction, Allyn and Bacon, Newton, MA, 1985. [§15]

    MATH  Google Scholar 

  15. H. Cohen and A.K. Lenstra, Implementation of a new primality test, Mathematics of Computation, 48 (1987) 103–121. [§18]

    MathSciNet  MATH  Google Scholar 

  16. G.L. Cohen, On the largest component of an odd perfect number, Journal of the Australian Mathematical Society (Series A), 42 (1987) 280–286. [§16]

    MATH  Google Scholar 

  17. R.E. Crandall, On the “3x+l” problem, Mathematics of Computation, 32 (1978) 1281–1292. [§19]

    MathSciNet  MATH  Google Scholar 

  18. M. Davis, Hilbert’s tenth problem is unsolvable, American Mathematical Monthly, 80 (1973) 233–269. [§20]

    MathSciNet  MATH  Google Scholar 

  19. M. Davis and R. Hersh, Hilberths lOth problem, Scientific American, 229:5 (Nov., 1973) 84–91. [§20]

    Google Scholar 

  20. M. Davis, Y. Matijasevic, and J. Robinson, Hilberths tenth problem. Diophantine equations: Positive aspects of a negative Solution, in Mathematical Developments Arising From Hilbert Problems, Proceedings of Symposia in Pure Mathematics, 28, Part 2, American Mathematical Society, Providence 1976, 323–378. [§20]

    Google Scholar 

  21. L.E. Dickson, History of the Theory of Numbers, vol. I, Chelsea, New York, 1971 (Nachdruck der Auflage von 1923). [§16]

    Google Scholar 

  22. L.E. Dickson, History of the Theory of Numbers, vol. II, Chelsea, New York, 1971 (Nachdruck der Auflage von 1923). [§14]

    Google Scholar 

  23. J. Dixon, Factorization and primality tests, American Mathematical Monthly, 91 (1984) 333–352. [§18]

    MATH  Google Scholar 

  24. V.H. Dyson, J.P. Jones, and J.C. Shepherdson, Some Diophantine forms of Gödel’s theorem, Archiv für Mathematische Logik und Grundlagenforschung, 22 (1982) 51–60. [§20]

    MathSciNet  MATH  Google Scholar 

  25. H.M. Edwards, Riemanris Zeta Function, Academic Press, New York, 1974. [§17]

    Google Scholar 

  26. H.M. Edwards, Fermat’s Last Theorem, A Genetic Introduction to Algebraic Number Theory, Springer, New York, 1977. [§13]

    MATH  Google Scholar 

  27. H.M. Edwards, Fermat’s last theorem, Scientific American, 239:4 (April, 1978) 104–122. [§13]

    Google Scholar 

  28. H.G. Eggleston, Note 2347. Isosceles triangles with integral sides and two integral medians, The Mathematical Gazette 37 (1953) 208–209. [§14]

    Google Scholar 

  29. N. Elkies, On A4 + B4 + C4 = D4, Mathematics of Computation, 51 (1988) 825–835. [§13]

    MathSciNet  MATH  Google Scholar 

  30. P. Erdös, The Solution in whole numbers of the equation 1/x 1 + … + 1/x N = a/b, Maternatikai Lapok, 1 (1950) 192–210. (Ungarisch, mit englischer Zusammenfassung; vgl. Math. Reviews 13 (1952) 208.) [§15]

    Google Scholar 

  31. P. Erdös and R. Graham, Old and New Problems and Results in Combinatorial Number Theory, Monographie No. 28 de L’Enseignement Mathematique, Universite de Geneve, Geneva 1980. [§15]

    MATH  Google Scholar 

  32. M. Filaseta, An application of Faltings’ results to Fermat’s last theorem, Comptes Rendus/Mathematical Reports, Academy of Science, Canada, 6 (1984) 31–32. [§13]

    MathSciNet  MATH  Google Scholar 

  33. D. Flath and S. Wagon, How to pick out the integers in the rationals: an application of number theory to logic, American Mathematical Monthly, 98 (1991). [§20]

    Google Scholar 

  34. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, San Francisco, W.H. Freeman, 1979. [§18]

    MATH  Google Scholar 

  35. L.E. Garner, On the Collatz 3n + 1 algorithm, Proceedings of the American Mathematical Society, 82 (1981) 19–22. [§19]

    MathSciNet  MATH  Google Scholar 

  36. R.L. Graham, On flnite sums of unit fractions, Proceedings ofthe London Mathematical Society, 14 (1964) 193–207. [§15]

    MATH  Google Scholar 

  37. R.L. Graham, B.L. Rothschild, and J.H. Spencer, Ramsey Theory, Wiley, New York, 1980. [§16]

    MATH  Google Scholar 

  38. A. Granville, The set of exponents, for which Fermat’s last theorem is true, has density one, Comptes Rendus/Mathematical Reports, Academy of Science, Canada, 7 (1985) 55–60. [§13]

    MathSciNet  MATH  Google Scholar 

  39. R. Güntsche, Über rationale Tetraeder, Archiv der Mathematik und Physik, 3 (1907) 371. [§14]

    Google Scholar 

  40. R.K. Guy, Unsolved Problems in Number Theory, Springer, New York, 1981. [§13]

    MATH  Google Scholar 

  41. P. Hagis, A lower bound for the set of odd perfect numbers, Mathematics of Computation, 27 (1973) 951–953. [§16]

    MathSciNet  MATH  Google Scholar 

  42. P. Hagis, Sketch of a proof that an odd perfect number relatively prime to 3 has at least eleven prime factors, Mathematics of Computation, 40 (1983) 399–404. [§16]

    MathSciNet  MATH  Google Scholar 

  43. L.-S. Hahn, Problems and solutions, Sugaku, Math. Soc. Japan, 31 (1979) 376 (Japanisch). [§15]

    Google Scholar 

  44. L.-S. Hahn, Egyptian fractions, Mathmedia, Academia Sinica, Taipei 15 (1980) 8–12 (Chinesisch). [§15]

    Google Scholar 

  45. G.H. Hardy and E.M. Wright, Einführung in die Zahlentheorie, Oldenbourg-Verlag, München, 1958. [§20]

    MATH  Google Scholar 

  46. T.L. Heath, The Thirteen Books ofEuclid’s Elements, vol. 2, Dover, New York, 1956. [§16]

    Google Scholar 

  47. D.R. Heath-Brown, Fermat’s last theorem for “almost all” exponents, Bulletin of the London Mathematical Society, 17 (1985) 15–16. [§13]

    MathSciNet  MATH  Google Scholar 

  48. D.R. Heath-Brown, The first case of Fermat’s last theorem, The Mathematical Intelligencer, 7 (1985) 40–47, 55. [§13]

    MathSciNet  MATH  Google Scholar 

  49. M.E. Hellman, The mathematics of public-key cryptography, Scientific American, 241:2 (Aug., 1979) 146–157. [§18]

    Google Scholar 

  50. J.M. Henle, An Outline of Set Theory, Springer, New York, 1986. [§20]

    MATH  Google Scholar 

  51. M. Iosifescu, On the random Riemann hypothesis, Proceedings of the Seventh Conference on Probability Theory, Brasov, Romania, 1982, Editura Academiei Republicii Socialiste Romania, Bucharest, 1984. [§17]

    Google Scholar 

  52. K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, New York, 1982. [§13]

    MATH  Google Scholar 

  53. Aleksandar Ivic, The Riemann Zeta-function, Wiley, New York, 1985. [§17]

    MATH  Google Scholar 

  54. J.P. Jones, Diophantine representation of the Fibonacci numbers, Fibonacci Quarterly, 13 (1975) 84–88. [§20]

    MathSciNet  MATH  Google Scholar 

  55. J.P. Jones, Universal Diophantine equation, Journal of Symbolic Logic, 47 (1982) 549–571. [§20]

    MathSciNet  MATH  Google Scholar 

  56. [JM1]J.P. Jones and Y.V. Matijasevic, Register machine proof of the theorem on exponential Diophantine representation of enumerable sets, Journal of Symbolic Logic, 49 (1984) 818–829. [§20]

    MathSciNet  MATH  Google Scholar 

  57. J.P. Jones and Y.V. Matijasevic, Proof of recursive unsolvability of Hilbert’s tenth problem, American Mathematical Monthly, 98 (1991) 689. [J.P. Jones, D. Sato, H. Wada, and D. Wiens, Diophantine representation of the set of prime numbers, American Mathematical Monthly, 83 (1976) 449–464. [§20]

    Google Scholar 

  58. L. Kirby and J. Paris, Accessible independence results for Peano Arithmetic, Bulletin ofthe London Mathematical Society, 14 (1982) 285–293. [§20]

    MathSciNet  MATH  Google Scholar 

  59. D.E. Knuth, The Art of Computer Programming, vol. 2, Addison-Wesley, Reading Mass., 1971. [§18]

    Google Scholar 

  60. I. Korec, Nonexistence of a small perfect rational cuboid, Acta Mathematica Universitatis Comenianae, 42–43 (1983) 73–86. [§14]

    MathSciNet  Google Scholar 

  61. I. Korec, Nonexistence of a small perfect rational cuboid, II, Acta Mathematica Universitatis Comenianae, 44–45 (1984) 39–48. [§14]

    MathSciNet  Google Scholar 

  62. J.C. Lagarias, The 3x + 1 problem and its generalizations, American Mathematical Monthly, 92 (1985) 3–23. [§19]

    MathSciNet  MATH  Google Scholar 

  63. J. Lagarias, V.S. Miller, and A. Odlyzko, Computing π(x): The Meissel-Lehmer method, Mathematics of Computation, 44 (1985) 537–560. [§17]

    MathSciNet  MATH  Google Scholar 

  64. E.J. Lee and J.S. Madachy, The history and discovery of amicable numbers IIII, Journal of Recreational Mathematics, 5 (1972) 77–93, 153–173, 231–249. [§16]

    Google Scholar 

  65. J. Leech, The rational cuboid revisited, American Mathematical Monthly, 84 (1977) 518–533. Corrections, ebenda 85 (1978) 473. [§14]

    MathSciNet  Google Scholar 

  66. N. MacKinnon and J. Eastmond, An attack on the Erdos conjecture, The Mathematical Gazette, 71 (1987) 14–19. [§16]

    MathSciNet  MATH  Google Scholar 

  67. K. Manders and L. Adleman, NP-complete decision problems for binary quadratics, Journal of Computer and System Sciences, 16 (1978) 168–184. [§20]

    MathSciNet  MATH  Google Scholar 

  68. H.B. Mann and W.A. Webb, A short proof of Fermat’s theorem for n = 3, The Mathematics Student, 46 (1978) 103–104. [§13]

    MathSciNet  Google Scholar 

  69. J. McCleary, How not to prove Fermat’s last theorem, American Mathematical Monthly, 96, (1989) 410–420. [§13]

    MathSciNet  MATH  Google Scholar 

  70. R.A. Melter, Problem 6628, American Malthematical Monthly, 97 (1990) 350. Solutions by C.R. Maderer, J.H. Steelman, J. Buddenhagen, ibid. (1991) (to appear). [§14]

    Google Scholar 

  71. E. Nagel and J.R. Newman, Gödel’s Proof University Press, New York, 1958. [§20]

    MATH  Google Scholar 

  72. I. Niven and H.S. Zuckerman, An Introduction to the Theory of Numbers, 2. Auflage, Wiley, New York, 1966. [§18]

    MATH  Google Scholar 

  73. A.M. Odlyzko, On the distribution of spacings between zeros of the zeta function, Mathematics of Computation, 48 (1987) 273–308. [§17]

    MathSciNet  MATH  Google Scholar 

  74. A.M. Odlyzko and H.J.J. te Riele, Disproof of the Mertens conjecture, Journal für die Reine und Angewandte Mathematik, 357 (1985) 138–160. [§17]

    MATH  Google Scholar 

  75. S.J. Patterson, An Introduction to the Theory of the Riemann Zeta-Function, Cambridge University Press, New York, 1988. [§17]

    MATH  Google Scholar 

  76. J. Pintz, An effective disproof of the Mertens conjecture, Asterisque, No. 147148 (1987) 325–333. [§17]

    MathSciNet  Google Scholar 

  77. C. Pomerance, Multiply perfect numbers, Mersenne primes, and effective computability, Mathematische Annalen, 226 (1977) 195–206. [§16]

    MathSciNet  MATH  Google Scholar 

  78. C. Pomerance, Recent developments in primality testing, The Mathematical Intelligencer, 3 (1981) 97–105. [§18]

    MathSciNet  MATH  Google Scholar 

  79. C. Pomerance, The search for prime numbers, Scientific American, 247 6 (Dec. 1982) 136–147. [§18]

    Google Scholar 

  80. C. Pomerance, Analysis and comparison of some integer factoring algorithms, in Computational Methods in Number Theory, Part I, H.W. Lenstra, R. Tijdeman, eds., Mathematical Centre Tracts 154, Amsterdam, 1982. [§18]

    Google Scholar 

  81. C. Pomerance, J.L. Selfridge, and S.S. Wagstaff, Jr., The pseudoprimes to 25 × 109, Mathematics of Computation, 35 (1980) 1003–1026. [§18]

    MathSciNet  MATH  Google Scholar 

  82. P.A. Pritchard, Long arithmetic progressions of primes; some old, some new, Mathematics of Computation, 45 (1985) 263–267. [§16]

    MathSciNet  MATH  Google Scholar 

  83. H.L. Resnikoff and R.O. Wells, Jr., Mathematics in Civilization, 2. Auflage, Dover, New York, 1984. [§15]

    Google Scholar 

  84. P. Ribenboim, Lectures on Fermat’s Last Theorem, Springer, New York, 1980. [§13]

    Google Scholar 

  85. P. Ribenboim, Recent results about Fermat’s last theorem, Expositiones Mathematicae, 5 (1987) 75–90. [§13]

    MathSciNet  MATH  Google Scholar 

  86. P. Ribenboim, The Book of Prime Number Records, Springer, New York, 1988. [§§15 and 17]

    MATH  Google Scholar 

  87. H. Riesel, Prime Numbers and Computer Methods for Factorization, Birkhäuser, Boston, 1985. [§16]

    MATH  Google Scholar 

  88. G. Robins and C.S. Shute, The Rhind Mathematical Papyrus, Dover, New York, 1987. [§15]

    MATH  Google Scholar 

  89. J. Robinson, Definability and decision problems in arithmetic, Journal of Symbolic Logic, 14 (1949) 98–114. [§20]

    MathSciNet  MATH  Google Scholar 

  90. R.M. Robinson, Advanced problem 6415, American Mathematical Monthly, 91 (1984) 373–374. [§20]

    Google Scholar 

  91. K.H. Rosen, Elementary Number Theory and its Applications, 2. Auflage, Addison-Wesley, Reading, Mass., 1987. [§§16 and 18]

    Google Scholar 

  92. M.I. Rosen, A proof of the Lucas-Lehmer test, American Mathematical Monthly, 95 (1988) 855–856. [§16]

    MathSciNet  MATH  Google Scholar 

  93. M.R. Schroeder, Number Theory in Science and Communication, Springer, Berlin, 1984. [§16]

    MATH  Google Scholar 

  94. B. Sturmfels, On the decidability of Diophantine problems in combinatorial geometry, Bulletin of the American Mathematical Society, 17 (1987)121–124. [§20]

    MathSciNet  MATH  Google Scholar 

  95. J.J. Sylvester, Note on a proposed addition to the vocabulary of ordinary arithmetic, Nature, 37 (1887) 152–153(Korrektur ebenda, S. 179). [§16]

    Google Scholar 

  96. J.J. Sylvester, On the divisors of the sum of a geometrical series whose first term is unity and common ratio any positive or negative integer, Nature, 37 (1888) 417–418. [§16]

    MATH  Google Scholar 

  97. H.J.J. te Riele, On generating new amicable pairs from given amicable pairs, Mathematics of Computation, 42 (1984) 219–223. [§16]

    MathSciNet  MATH  Google Scholar 

  98. H.J.J. te Riele, Computation of all the amicable pairs below 1011, Mathematics of Computation, 47 (1986) 361–368. [§16]

    MathSciNet  MATH  Google Scholar 

  99. H.J.J. te Riele, On the sign of the difference π(x) − li(x), Mathematics of Computation, 48 (1987) 323–328. [§17]

    MathSciNet  MATH  Google Scholar 

  100. R. Terras, A stopping time problem on the positive integers, Acta Arithmetica, 30 (1976) 241–252. [§19]

    MathSciNet  MATH  Google Scholar 

  101. J.W. Tanner and S.S. Wagstaff, Jr., New congruences for the Bernoulli numbers, Mathematics of Computation, 48 (1987) 341–350. [§13]

    MathSciNet  MATH  Google Scholar 

  102. J.W. Tanner and S.S. Wagstaff, Jr., New bound for the first case of Fermat’s last theorem, Mathematics of Computation, 53 (1989) 743–750. [§13]

    MathSciNet  MATH  Google Scholar 

  103. M. Vose, Egyptian fractions, Bulletin of the London Mathematical Society, 17 (1985) 21–24. [§15]

    MathSciNet  MATH  Google Scholar 

  104. S. Wagon, The evidence: The Collatz problem, The Mathematical Intelligencer, 7:1 (1985) 72–76. [§19]

    MathSciNet  MATH  Google Scholar 

  105. S. Wagon, The evidence: Odd perfect numbers, The Mathematical Intelligencer, 7:2 (1985) 66–68. [§16]

    MathSciNet  MATH  Google Scholar 

  106. S. Wagon, The evidence: Fermat’s last theorem, The Mathematical Intelligencer, 8:1 (1986) 59–61. [§13]

    MathSciNet  MATH  Google Scholar 

  107. S. Wagon, The evidence: Primality testing, The Mathematical Intelligencer, 8:3 (1986) 58–61. [§18]

    MathSciNet  MATH  Google Scholar 

  108. S. Wagon, The evidence: Where are the zeros of zeta of s?, The Mathematical Intelligencer, 8:4 (1986) 57–62. [§17]

    MathSciNet  MATH  Google Scholar 

  109. S. Wagon, Mathematica in Action, W.H. Freeman, New York, 1991. [§§16 and 17]

    MATH  Google Scholar 

  110. S.S. Wagstaff, Jr., The irregulär primes to 125000, Mathematics of Computation, 32 (1978) 583–591. [§13]

    MathSciNet  MATH  Google Scholar 

  111. A. Weil, Number Theory: An Approach Through History; From Hammurapi to Legendre, Birkhäuser, Boston, 1983. [§13]

    Google Scholar 

  112. H.C. Williams, An overview of factoring, in Advances in Cryptology, D. Chaum, ed., Plenum, 1984. [§18]

    Google Scholar 

  113. J. Young and D.A. Buell, The twentieth Fermat number is composite, Mathematics of Computation, 50 (1988) 261–263. [§16]

    MathSciNet  MATH  Google Scholar 

  114. D. Zagier, The first 50 million prime numbers, The Mathematical Intelligencer, 0 (1977) 7–19. [§16]

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Washington, USA

    Victor Klee

  2. Macalester College, USA

    Stan Wagon

Authors
  1. Victor Klee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stan Wagon
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Basel AG

About this chapter

Cite this chapter

Klee, V., Wagon, S. (1997). Zahlentheorie. In: Alte und neue ungelöste Probleme in der Zahlentheorie und Geometrie der Ebene. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6073-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-6073-4_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-5308-7

  • Online ISBN: 978-3-0348-6073-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation