2-Selmer groups of quadratic twists of elliptic curves
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- by George Boxer and Peter Diao PDF
- Proc. Amer. Math. Soc. 138 (2010), 1969-1978 Request permission
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.References
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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
- Received by editor(s): October 27, 2009
- Published electronically: February 11, 2010
- Communicated by: Ken Ono
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1969-1978
- MSC (2010): Primary 11G05, 11G40
- DOI: https://doi.org/10.1090/S0002-9939-10-10273-1
- MathSciNet review: 2596031