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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Book Information:

Author: Serge Lang
Title: Introduction to modular forms
Additional book information: A Series of Comprehensive Studies in Mathematics, No. 222, Springer-Verlag, Berlin and New York, 1976, ix + 261 pp.

References [Enhancements On Off] (What's this?)

  • 1. Walter L. Baily Jr., Introductory lectures on automorphic forms, Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1973. Kanô Memorial Lectures, No. 2; Publications of the Mathematical Society of Japan, No. 12. MR 0369750
  • 2. A. Borel, S. Chowla, C. S. Herz, K. Iwasawa, and J.-P. Serre, Seminar on complex multiplication, Seminar held at the Institute for Advanced Study, Princeton, N.J., 1957-58. Lecture Notes in Mathematics, No. 21, Springer-Verlag, Berlin-New York, 1966. MR 0201394
  • 3. Proceedings of Symposia in Pure Mathematics. Vol. IX: Algebraic groups and discontinuous subgroups, Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society held at the University of Colorado, Boulder, Colorado (July 5-August 6, vol. 1965, American Mathematical Society, Providence, R.I., 1966. MR 0202512
  • 4. A. Borel and W. Casselman, Automorphic forms, representations and L-functions, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, R. I., 1979.
  • 5. Felix E. Browder (ed.), Mathematical developments arising from Hilbert problems, Proceedings of Symposia in Pure Mathematics, Vol. XXVIII, American Mathematical Society, Providence, R. I., 1976. MR 0419125
  • 6. Pierre Deligne and Willem Kuyk (eds.), Modular functions of one variable. II, Lecture Notes in Mathematics, Vol. 349, Springer-Verlag, Berlin-New York, 1973. MR 0330050
  • 7. H. Dym and H. P. McKean, Fourier series and integrals, Academic Press, New York-London, 1972. Probability and Mathematical Statistics, No. 14. MR 0442564
  • 8. A. Fröhlich (ed.), Algebraic number fields: 𝐿-functions and Galois properties, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1977. MR 0437486
  • 9. I. M. Gelfand, M. I. Graev and I. I. Piatetskii-Shapiro, Automorphic functions and representation theory, Saunders, Chicago, Ill., 1969.
  • 10. E. Hecke, Dirichlet series, modular functions and quadratic forms (IAS Lectures), Edwards Bros., Ann Arbor, Mich., 1938.
  • 11. K. Imai, Generalization of Hecke's correspondence, Ph.D. Thesis, Univ. of California, San Diego, 1979.
  • 12. Kenkichi Iwasawa, Lectures on 𝑝-adic 𝐿-functions, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Annals of Mathematics Studies, No. 74. MR 0360526
  • 13. Joseph Lehner, Discontinuous groups and automorphic functions, Mathematical Surveys, No. VIII, American Mathematical Society, Providence, R.I., 1964. MR 0164033
  • 14. Stephen Lichtenbaum, Values of zeta-functions, étale cohomology, and algebraic 𝐾-theory, Algebraic 𝐾-theory, II: “Classical” algebraic 𝐾-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Springer, Berlin, 1973, pp. 489–501. Lecture Notes in Math., Vol. 342. MR 0406981
  • 15. Hans Maass, Lectures on modular functions of one complex variable, Notes by Sunder Lal. Tata Institute of Fundamental Research Lectures on Mathematics, No. 29, Tata Institute of Fundamental Research, Bombay, 1964. MR 0218305
  • 16. Hans Maass, Siegel’s modular forms and Dirichlet series, Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin-New York, 1971. Dedicated to the last great representative of a passing epoch. Carl Ludwig Siegel on the occasion of his seventy-fifth birthday. MR 0344198
  • 17. Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
  • 18. J.-P. Serre, A course in arithmetic, Springer-Verlag, New York-Heidelberg, 1973. Translated from the French; Graduate Texts in Mathematics, No. 7. MR 0344216
  • 19. A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87. MR 0088511
  • 20. Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Kanô Memorial Lectures, No. 1. MR 0314766
  • 21. Takuro Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), no. 2, 393–417. MR 0427231
  • 22. Carl Ludwig Siegel, Gesammelte Abhandlungen. Bände I, II, III, Herausgegeben von K. Chandrasekharan und H. Maass, Springer-Verlag, Berlin-New York, 1966 (German). MR 0197270
  • 23. C. L. Siegel, Topics in complex function theory. Vol. I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. Elliptic functions and uniformization theory; Translated from the German by A. Shenitzer and D. Solitar; With a preface by Wilhelm Magnus; Reprint of the 1969 edition; A Wiley-Interscience Publication. MR 1008930
  • 24. H. M. Stark, The analytic theory of algebraic numbers, Bull. Amer. Math. Soc. 81 (1975), no. 6, 961–972. MR 0444611,
  • 25. H. M. Stark, 𝐿-functions at 𝑠=1. III. Totally real fields and Hilbert’s twelfth problem, Advances in Math. 22 (1976), no. 1, 64–84. MR 0437501,
  • 26. Audrey Terras, Applications of special functions for the general linear group to number theory, Séminaire Delange-Pisot-Poitou, 18e année: 1976/77, Théorie des nombres, Fasc. 2, Secrétariat Math., Paris, 1977, pp. Exp. No. 23, 16. MR 551347
  • 27. Nolan R. Wallach, Symplectic geometry and Fourier analysis, Math Sci Press, Brookline, Mass., 1977. With an appendix on quantum mechanics by Robert Hermann; Lie Groups: History, Frontiers and Applications, Vol. V. MR 0488148
  • 28. André Weil, Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 168 (1967), 149–156 (German). MR 0207658,

Review Information:

Reviewer: Audrey Terras
Journal: Bull. Amer. Math. Soc. 2 (1980), 206-214