Bulletin of the American Mathematical Society

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Book Information:

Author: Haruzo Hida
Title: Elementary theory of -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

1.

A. Beilinson, Higher regulators and values of -functions, J. Soviet Math. 30 (1985), 2036-2070.

Spencer Bloch and Kazuya Kato, $L$-functions and Tamagawa numbers of motives, The Grothendieck Festschrift, Vol. I, Progr. Math., vol. 86, Birkhäuser Boston, Boston, MA, 1990, pp. 333–400. MR 1086888

J. Coates and A. Wiles, On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977), no. 3, 223–251. MR 463176, DOI 10.1007/BF01402975

P. Deligne, Valeurs de fonctions $L$ et périodes d’intégrales, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 313–346 (French). With an appendix by N. Koblitz and A. Ogus. MR 546622

Benedict H. Gross and Don B. Zagier, Heegner points and derivatives of $L$-series, Invent. Math. 84 (1986), no. 2, 225–320. MR 833192, DOI 10.1007/BF01388809

B. Mazur, J. Tate, and J. Teitelbaum, On $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math. 84 (1986), no. 1, 1–48. MR 830037, DOI 10.1007/BF01388731

B. Mazur and A. Wiles, Class fields of abelian extensions of $\textbf {Q}$, Invent. Math. 76 (1984), no. 2, 179–330. MR 742853, DOI 10.1007/BF01388599

M. Rapoport, N. Schappacher, and P. Schneider (eds.), Beilinson’s conjectures on special values of $L$-functions, Perspectives in Mathematics, vol. 4, Academic Press, Inc., Boston, MA, 1988. MR 944987

Karl Rubin, The “main conjectures” of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991), no. 1, 25–68. MR 1079839, DOI 10.1007/BF01239508

Karl Rubin, Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 64 (1981), no. 3, 455–470. MR 632985, DOI 10.1007/BF01389277

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.

Richard Taylor and Andrew Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), no. 3, 553–572. MR 1333036, DOI 10.2307/2118560

Andrew Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551. MR 1333035, DOI 10.2307/2118559

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 , 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