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Book Review

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Book Information:

Author: Haruzo Hida
Title: Elementary theory of $L$-functions and Eisenstein series
Additional book information: London Mathematical Society Student Texts, Vol. 26, Cambridge University Press, Cambridge, 1993, x + 386 pp., ISBN 0-521-43411-4, $69.95, hardback; ISBN 0-521-43569-2, paperback

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

  • 1. A. Beilinson, Higher regulators and values of $L$-functions, J. Soviet Math. 30 (1985), 2036-2070.
  • 2. S. Bloch, K. Kato, $L$-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 $L$ 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 $L$-series, Invent. Math. 84 (1986), 225-320. MR 87j:11057
  • 6. B. Mazur, J. Tate, J. Teitelbaum, On $p$-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 $L$-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

Review Information:

Reviewer: Glenn Stevens
Affiliation: Boston University
Journal: Bull. Amer. Math. Soc. 34 (1997), 67-71
MSC (1991): Primary 11Fxx
Review copyright: © Copyright 1997 American Mathematical Society
American Mathematical Society