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The average analytic rank of elliptic curves

Abstract:

All the results in this paper are conditional on the Riemann hypothesis for the L-functions of elliptic curves. Under this assumption, we show that the average analytic rank of all elliptic curves over ℚ is at most 2, thereby improving a result of Brumer. We also show that the average within any family of quadratic twists is at most 3/2, improving a result of Goldfeld. A third result concerns the density of curves with analytic rank at least R and shows that the proportion of such curves decr...

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Published

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
DUKE MATHEMATICAL JOURNAL
Volume:
122
Issue:
3
Pages:
591-623
Publication date:
2004-04-15
DOI:
ISSN:
0012-7094
URN:
uuid:d1991ae1-6389-4a31-a02e-c80428af7515
Source identifiers:
24306
Local pid:
pubs:24306
Language:
English

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