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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

2-Selmer groups of quadratic twists of elliptic curves


Authors: George Boxer and Peter Diao
Journal: Proc. Amer. Math. Soc. 138 (2010), 1969-1978
MSC (2010): Primary 11G05, 11G40
Published electronically: February 11, 2010
MathSciNet review: 2596031
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Abstract: In this paper we investigate families of quadratic twists of elliptic curves. Addressing a speculation of Ono, we identify a large class of elliptic curves for which the parities of the ``algebraic parts'' of the central values $ L(E^{(d)}/\mathbb{D}{Q},1)$, as $ d$ varies, have essentially the same multiplicative structure as the coefficients $ a_d$ of $ L(E/\mathbb{D}{Q},s)$. We achieve this by controlling the 2-Selmer rank (à la Mazur and Rubin) when the Tamagawa numbers do not already dictate the parity.


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Additional Information

George Boxer
Affiliation: Department of Mathematics, Mailbox 2704, Frist Center, Princeton University, Princeton, New Jersey 08544
Email: gboxer@princeton.edu

Peter Diao
Affiliation: Department of Mathematics, Mailbox 2704, Frist Center, Princeton University, Princeton, New Jersey 08544
Email: pdiao@princeton.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10273-1
PII: S 0002-9939(10)10273-1
Received by editor(s): October 27, 2009
Published electronically: February 11, 2010
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.