|
A nonvanishing theorem for derivatives of automorphic $L$-functions with applications to elliptic curves
Author(s):
Daniel
Bump;
Solomon
Friedberg;
Jeffrey
Hoffstein
Journal:
Bull. Amer. Math. Soc.
21
(1989),
89-93.
MSC (1985):
Primary 11G40;
Secondary 11F11, 11F46, 11F67
MathSciNet review:
983456
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- 1.
- D. Blasius, A. Clozel and D. Ramakrishnan, Algébricité de l'action des opérateurs de Hecke sur certaines formes de Maass, C. R. Acad. Sci. Paris 305 (1987), 705-708. MR 920047
- 2.
- D. Bump, S. Friedberg and J. Hoffstein, Eisenstein series on the metaplectic group and nonvanishing theorems for automorphic L-functions and their derivatives, Ann. of Math. (2) (to appear). MR 1038358
- 3.
- J. Coates and A. Wiles, On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977), 223-251. MR 463176
- 4.
- M. Eichler and D. Zagier, The theory of Jacobi forms, Birkhäuser, 1985. MR 781735
- 5.
- D. Goldfeld, Gauss' class number problem for imaginary quadratic fields, Bull. Amer. Math. Soc. (N.S.) 13 (1985), 23-37. MR 788386
- 6.
- D. Goldfeld and J. Hoffstein, Eisenstein series of 1/2-integral weight and the mean value of real Dirichlet L-series, Invent. Math. 80 (1985), 185-208. MR 788407
- 7.
- D. Goldfeld, J. Hoffstein and S. Patterson, On automorphic functions of half-integral weight with applications to elliptic curves, Number Theory Related to Fermat's Last Theorem (N. Koblitz, ed.), 1982, pp,. 153-194. MR 685295
- 8.
- D. Gross and D. Zagier, Heegner points and derivatives of L-series, Invent. Math. 84 (1986), 225-320. MR 833192
- 9.
- R. Howe, θ-series and invariant theory, Automorphic Forms, Representations and L-functions, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc. Providence, R.I., 1979, pp. 275-285. MR 546602
- 10.
- H. Jacquet, J. Shalika and I. Piatetski-Shapiro, in preparation.
- 11.
- V. Kolyvagin, On groups of Mordell-Weil and Shafarevich-Tate and Weil elliptic curves, Preprint, (1988) (Russian).
- 12.
- M. Novodvorsky, Automorphic L-functions for the symplectic group GSp4, "Automorphic Forms, Representations and L-functions, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, R.I., 1979, pp. 87-95. MR 546610
- 13.
- D. Rohrlich, Nonvanishing of L-functions for GL(2), Invent. Math, (to appear). MR 1001846
- 14.
- G. Shimura, On the periods of modular forms, Math. Ann. 229 (1977), 211-221. MR 463119
- 15.
- J. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math. 72 (1983), 323-334. MR 700775
- 16.
- J. Waldspurger, Correspondence de Shimura, J. Math. Pures Appl. 59 (1980), 1-132. MR 577010
- 17.
- J. Waldspurger, Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. 60 (1981), 375-484. MR 646366
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1985):
11G40, 11F11, 11F46, 11F67
Retrieve articles in all Journals with MSC
(1985):
11G40, 11F11, 11F46, 11F67
Additional Information:
DOI:
10.1090/S0273-0979-1989-15771-6
PII:
S 0273-0979(1989)15771-6
|