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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Average size of $ 2$-Selmer groups of elliptic curves, I


Author: Gang Yu
Journal: Trans. Amer. Math. Soc. 358 (2006), 1563-1584
MSC (2000): Primary 11G05, 14H52
Published electronically: October 31, 2005
MathSciNet review: 2186986
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Abstract: In this paper, we study a class of elliptic curves over $ \mathbb{Q}$ with $ \mathbb{Q}$-torsion group $ {\mathbb{Z}}_{2}\times\mathbb{Z}_{2}$, and prove that the average order of the $ 2$-Selmer groups is bounded.


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Additional Information

Gang Yu
Affiliation: Department of Mathematics, LeConte College, 1523 Greene Street, University of South Carolina, Columbia, South Carolina 29208
Email: yu@math.sc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03806-7
PII: S 0002-9947(05)03806-7
Keywords: Elliptic curves, $2$-descent procedure, character sums
Received by editor(s): September 16, 2000
Received by editor(s) in revised form: May 2, 2004
Published electronically: October 31, 2005
Article copyright: © Copyright 2005 American Mathematical Society