A note on a question of J. Nekovár

and the Birch and Swinnerton-Dyer conjecture

Author:
Ken Ono

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2849-2853

MSC (1991):
Primary 11G40; Secondary 14G10

DOI:
https://doi.org/10.1090/S0002-9939-98-04465-7

MathSciNet review:
1459142

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a square-free integer, then let denote the elliptic curve over given by the equation

Let denote the Hasse-Weil -function of , and let denote the `algebraic part' of the central critical value . Using a theorem of Sturm, we verify a congruence conjectured by J. Neková\v{r}. By his work, if denotes the 3-Selmer group of and is a square-free integer with , then we find that

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Additional Information

**Ken Ono**

Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540;
Department of Mathematics, Penn State University, University Park, Pennsylvania 16802

Email:
ono@math.ias.edu, ono@math.psu.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04465-7

Keywords:
Elliptic curves,
modular forms

Received by editor(s):
March 13, 1997

Additional Notes:
The author is supported by National Science Foundation grants DMS-9304580 and DMS-9508976, and NSA grant MSPR-YO12.

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 1998
American Mathematical Society