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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
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?)

P. Garrett, Decomposition of Eisenstein series: Rankin triple products, Ann. of Math., 125 (1987), 209-235. MR 0881269
A. Hurwitz, Über die Entwicklungskoefficienten der lemniskatischen Fuktionen, Math. Ann. 51 (1899), 196-226. (=Werke, Band II, LXVII)
A. W. Knapp, Representation theory of semisimple groups, Princeton Mathematical Series 36, Princeton University Press, 1986. MR 0855239
R. P. Langlands, On the functional equation satisfied by Eisenstein series, Lecture notes in Math. 544, Springer, 1976. MR 0579181
Y. I. Manin, Periods of parabolic forms and $p$-adic Hecke series, Math. USSR Sbornik, 21 (1973), 371-393.
G. Shimura, Sur les intégrales attachées aux formes automorphes, J. Math. Soc. Japan, 11 (1959), 291-311. MR 0120372
G. Shimura, Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton University Press, 1971. MR 0314766
G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. (3) 31 (1975), 79-98. MR 0382176
G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure and Applied Math. 29 (1976), 783-804. MR 0434962
G. Shimura, Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982), 269-302. MR 0669297
G. Shimura, Euler products and Eisenstein series, CBMS Regional Conference Series in Mathematics, Number 93, 1997, American Mathematical Society. MR 1450866
J. Sturm, The critical values of zeta functions associated to the symplectic group, Duke Math. J. 48(1981), 327-350. MR 0620253
A. Weil, Number theory, an approach through history, Birkhäuser, 1984. MR 0734177

Review Information:

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