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Average size of  -Selmer groups of elliptic curves, I
Author:
Gang Yu
Journal:
Trans. Amer. Math. Soc. 358 (2006), 1563-1584
MSC (2000):
Primary 11G05, 14H52
Posted:
October 31, 2005
MathSciNet review:
2186986
Full-text PDF Free Access
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Additional Information
Abstract: In this paper, we study a class of elliptic curves over  with  -torsion group  , and prove that the average order of the  -Selmer groups is bounded.
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-, Average size of
 -Selmer groups of elliptic curves, II, to appear in Acta Arith.
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- R. Bölling, Die Ordnung der Schafarewitsch-Tate Gruppe kann beliebig gross werden, Math. Nachr. 67 (1975), 157-179. MR 0384812 (52:5684)
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- A. Brumer, The average rank of elliptic curves, I, Invent. Math 109 (1992), 445-472. MR 1176198 (93g:11057)
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 -series, II, Proc. Lond. Math. Soc., III. Ser.13, (1963), 524-536. MR 0148626 (26:6133)
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- H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, 1974. MR 0424730 (54:12689)
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- D. R. Heath-Brown, The size of Selmer groups for the congruent number problem I, Invent. Math. 111 (1) (1993), 171-195. MR 1193603 (93j:11038)
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- A. Selberg, Note on a paper by L. G. Sathe, J. Indian Math. Soc. 18 (1954), 83-87. MR 0067143 (16:676a)
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- G. Yu, Rank 0 quadratic twists of a family of elliptic curves, Compositio Math 135 (3) (2003), 331-356. MR 1956817 (2004b:11082)
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- -, Average size of -Selmer groups of elliptic curves, II, to appear in Acta Arith.
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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
Posted:
October 31, 2005
Article copyright:
© Copyright 2005 American Mathematical Society
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