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On the low-lying zeros of Hasse–Weil L-functions for elliptic curves.

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On the low-lying zeros of Hasse–Weil L-functions for elliptic curves.

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dc.contributor.author Baier, Stephan.
dc.contributor.author Zhao, Liangyi.
dc.date.accessioned 2009-04-09T03:06:30Z
dc.date.available 2009-04-09T03:06:30Z
dc.date.copyright 2008
dc.date.issued 2009-04-09T03:06:30Z
dc.identifier.citation Baier, S. & Zhao, L. (2008). On the low-lying zeros of Hasse–Weil L-functions for elliptic curves. Advances in Mathematics, 219(3), 952-985.
dc.identifier.issn 0001-8708
dc.identifier.uri http://hdl.handle.net/10220/4556
dc.description.abstract In this paper, we obtain an unconditional density theorem concerning the low-lying zeros of Hasse-Weil L-functions for a family of elliptic curves. From this together with the Riemann hypothesis for these L-functions, we infer the majorant of 27/14 (which is strictly less than 2) for the average rank of the elliptic curves in the family under consideration. This upper bound for the average rank enables us to deduce that, under the same assumption, a positive proportion of elliptic curves have algebraic ranks equaling their analytic ranks and finite Tate-Shafarevic group. Statements of this flavor were known previously under the additional assumptions of GRH for Dirichlet L-functions and symmetric square L-functions which are removed in the present paper.
dc.format.extent 25 p.
dc.language.iso en
dc.relation.ispartofseries Advances in Mathematics.
dc.subject DRNTU::Science::Mathematics::Number theory.
dc.title On the low-lying zeros of Hasse–Weil L-functions for elliptic curves.
dc.type Journal Article
dc.contributor.school School of Physical and Mathematical Sciences
dc.identifier.openurl http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rft.object_id=954922644001&sfx.request_id=186124&sfx.ctx_obj_item=1
dc.description.version Accepted version

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