The Arithmetic of Number Fields

  • Emil Grosswald
Part of the Modern Birkhäuser Classics book series (MBC)


In Chapters 8 and 9 the reader had ample opportunity to convince himself that tools like the theory of functions of a complex variable, or Tauberian theorems, can be very useful in handling seemingly unrelated problems like the number π(x) of primes up to x. These same theories, while hardly mentioned in Chapter 7, have been found to be needed in the treatment of certain partition problems.


Number Field Algebraic Number Diophantine Equation Principal Ideal Algebraic Integer 
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  1. 1.
    W. W. Adams and L. J. Goldstein, Introduction to Number Theory, Englewood Cuffs, N.J.: Prentice Hall, 1976.MATHGoogle Scholar
  2. 2.
    A. B. Ayoub, On the Fundamental Units of Prime Cyclotomic Fields. Unpublished dissertation, Temple University, 1980.Google Scholar
  3. 3.
    P. Barrucand and H. Cohn, Journal of Number Theory, 2, 1970, pp. 7–21.CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    L. Bernstein and H. Hasse, Pacific Journal of Math., 30, 1969, pp. 293–365.CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    G. Birkhoff and S. MacLane, A Survey of Modern Algebra, New York: Macmillan, 1959.Google Scholar
  6. 6.
    A. L. Cauchy, Comptes Rendus de l’Acad. des Sciences (Paris), 24, (1947) pp. 578–584.Google Scholar
  7. 7.
    H. Chatland and H. Davenport, Canadian Journal of Math., 2,1950, pp. 289–296.CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    L. E. Dickson, History of the Theory of Numbers, New York: Chelsea Publishing Co., 1952.Google Scholar
  9. 9.
    G. L. Dirichlet, Memoire read at the Académie Royale des Sciences (Institut de France) on July 11, 1825; published in the Journal f. d. reine, u. angew. Mathem., 3,1828, pp. 354–357 Werke, vol 1, pp. 21–46.Google Scholar
  10. 10.
    C. F. Gauss, Disquisitiones Arith., (Translated from the second Latin edition, 1870, by A. Clark). New Haven: Yale University Press, 1966.Google Scholar
  11. 11.
    E. S. Golod and I. R. Shafarevich, Izvestiya Akad. Nauk SSSR Ser. Mat., 28, 1964, pp. 261–272.MATHGoogle Scholar
  12. 12.
    G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford: The Clarendon Press, 1960.MATHGoogle Scholar
  13. 13.
    E. Hecke, Theorie der algebraischen Zahlen, Leipzig: Akad. Verlagsgesellschaft, 1923MATHGoogle Scholar
  14. 13a.
    E. Hecke, Theorie der algebraischen Zahlen, New York: Chelsea Publishing Co., 1948.MATHGoogle Scholar
  15. 14.
    I. N. Herstein, Topics in Algebra, Waltham, Mass.: Ginn & Co., 1964.MATHGoogle Scholar
  16. 15.
    E. E. Kummer,Collected Papers, Vol I. Edited by André Weil. New York: Springer Verlag, 1975.Google Scholar
  17. 16.
    A. M. Legendre, Essai sur la Théorie des Nombres, Paris: Duprat, 1808. (Legendre gives credit for many results to Sophie Germaine).Google Scholar
  18. 17.
    H. W. Lenstra, Mathematical Intelligencer, 2, 1979, pp. 6–15, 73–77, 99–103.CrossRefMATHMathSciNetGoogle Scholar
  19. 18.
    J. M. Masley, Inventiones Mathematica, 28, 1975, pp. 243–244;CrossRefMATHMathSciNetGoogle Scholar
  20. 18a.
    J. M. Masley, Composito Mathematica, 33, 1976, pp. 179–186; see also dissertation, Princeton University.MATHMathSciNetGoogle Scholar
  21. 19.
    J. M. Masley and H. L. Montgomery,Journal f. d. reine u. angew. Mathem., 286/287,1976, pp. 248–256.MathSciNetGoogle Scholar
  22. 20.
    R. Pollard, The Theory of Algebraic Numbers (Cams Monograph No. 9). New York: J. Wiley & Sons, 1950.MATHGoogle Scholar
  23. 21.
    P. Roquette, Proceedings of the International Conference on Algebraic Number Theory, London Math. Soc. (NATO Advanced Study Institute) and International Mathem. Union. Edited by J. W. S. Cassel and A. Fröhlich. London: Academic Press. Washington, D.C.: Thompson Book Co., 1967, pp. 231–249.Google Scholar
  24. 22.
    C. L. Siegel, Lectures on advanced, analytic number theory. Bombay: Tata Institute of Fundam. Research 1965.MATHGoogle Scholar
  25. 23.
    B. L. van der Waerden, Modern Algebra (2 vol.), New York, F. Ungar, 1950.Google Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • Emil Grosswald
    • 1
  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA

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