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Book Review

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Book Information:

Author: Goro Shimura
Title: Arithmeticity in the theory of automorphic forms
Additional book information: Mathematical Surveys and Monographs, vol. 82, American Mathematical Society, Providence, RI, x+302 pp., ISBN 0-8218-2671-9, $69.00

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

  • 1. Paul B. Garrett, Decomposition of Eisenstein series: Rankin triple products, Ann. of Math. (2) 125 (1987), no. 2, 209–235. MR 881269, 10.2307/1971310
  • 2. A. Hurwitz, Über die Entwicklungskoefficienten der lemniskatischen Fuktionen, Math. Ann. 51 (1899), 196-226. (=Werke, Band II, LXVII)
  • 3. Anthony W. Knapp, Representation theory of semisimple groups, Princeton Mathematical Series, vol. 36, Princeton University Press, Princeton, NJ, 1986. An overview based on examples. MR 855239
  • 4. Robert P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Mathematics, Vol. 544, Springer-Verlag, Berlin-New York, 1976. MR 0579181
  • 5. Y. I. Manin, Periods of parabolic forms and $p$-adic Hecke series, Math. USSR Sbornik, 21 (1973), 371-393.
  • 6. Goro Shimura, Sur les intégrales attachées aux formes automorphes, J. Math. Soc. Japan 11 (1959), 291–311 (French). MR 0120372
  • 7. 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. Kan\cflex o Memorial Lectures, No. 1. MR 0314766
  • 8. Goro Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. (3) 31 (1975), no. 1, 79–98. MR 0382176
  • 9. Goro Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. Math. 29 (1976), no. 6, 783–804. MR 0434962
  • 10. Goro Shimura, Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982), no. 3, 269–302. MR 669297, 10.1007/BF01461465
  • 11. Goro Shimura, Euler products and Eisenstein series, CBMS Regional Conference Series in Mathematics, vol. 93, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1997. MR 1450866
  • 12. Jacob Sturm, The critical values of zeta functions associated to the symplectic group, Duke Math. J. 48 (1981), no. 2, 327–350. MR 620253
  • 13. André Weil, Number theory, Birkhäuser Boston, Inc., Boston, MA, 1984. An approach through history; From Hammurapi to Legendre. MR 734177

Review Information:

Reviewer: Hiroyuki Yoshida
Affiliation: Kyoto University
Email: yoshida@kusm.kyoto-u.ac.jp
Journal: Bull. Amer. Math. Soc. 39 (2002), 441-448
Published electronically: April 15, 2002
Review copyright: © Copyright 2002 American Mathematical Society