A note on a question of J. Nekovár and the Birch and SwinnertonDyer conjecture
Author:
Ken Ono
Journal:
Proc. Amer. Math. Soc. 126 (1998), 28492853
MSC (1991):
Primary 11G40; Secondary 14G10
MathSciNet review:
1459142
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Abstract: If is a squarefree integer, then let denote the elliptic curve over given by the equation Let denote the HasseWeil 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 3Selmer group of and is a squarefree 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:
http://dx.doi.org/10.1090/S0002993998044657
PII:
S 00029939(98)044657
Keywords:
Elliptic curves,
modular forms
Received by editor(s):
March 13, 1997
Additional Notes:
The author is supported by National Science Foundation grants DMS9304580 and DMS9508976, and NSA grant MSPRYO12.
Communicated by:
David E. Rohrlich
Article copyright:
© Copyright 1998 American Mathematical Society
