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Book Information

Author(s): Haruzo Hida
Title: Elementary theory of $L$

-functions and Eisenstein series
Additional book information: London Mathematical Society Student Texts, Cambridge University Press, Cambridge, Vol. 26, 1993, x + 386 pp., (hardback) $69.95, ISBN 0-521-43411-4 ; (paperback) ISBN 0-521-43569-2

1.: A. Beilinson, Higher regulators and values of -functions, J. Soviet Math. 30 (1985), 2036-2070.
2.: S. Bloch, K. Kato, -functions and Tamagawa numbers of motives, The Grothendieck Festschrift, Volume I, Progress in Mathematics, vol. 86, 1990, pp. 333-400. MR 92g:11063
3.: J. Coates, A. Wiles, On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977), 223-251. MR 57:3134
4.: P. Deligne, Valeurs de fonctions et périodes d'integrales, Proc. Symp. Pure Math. 33 (1979), Part 2, 313-346. MR 81d:12009
5.: B. Gross, D. Zagier, Heegner points and derivatives of -series, Invent. Math. 84 (1986), 225-320. MR 87j:11057
6.: B. Mazur, J. Tate, J. Teitelbaum, On -adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math. 84 (1986), 1-48. MR 87e:11076
7.: B. Mazur, A. Wiles, Class fields of abelian extensions of ${\mathbf {Q}}$ , Invent. Math. 76 (1984), 179-330. MR 85m:11069
8.: M. Rapoport, N. Schappacher, P. Schneider (editors), Beilinson's Conjectures on Special Values of -functions, Perspectives in Mathematics 4, Academic Press, 1988. MR 89a:14002
9.: K. Rubin, The ``main conjectures" of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991), 25-68. MR 92f:11151
10.: -, Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 64 (1981), 455-470. MR 83f:10034
11.: J. Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog, Sem. Bourbaki exposé 306, 1965-66, Dix exposés sur la cohomologie des Schémas, North Holland, 1968.
12.: R. Taylor, A. Wiles, Ring-theoretic properties of certain Hecke algebras, Annals of Math. 141 (1995), 553-572. MR 96d:11072
13.: A. Wiles, Modular elliptic curves and Fermat's Last Theorem, Annals of Math. 141 (1995), 443-551. MR 96d:11071

Reviewer(s):
Glenn Stevens
Affiliation: Boston University
Email: ghs@math.bu.edu

MSC (1991): Primary 11Fxx
DOI: 10.1090/S0273-0979-97-00696-4
PII: S 0273-0979(97)00696-4
Copyright of article: Copyright 1997, American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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