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

• Main Authors: Baier, Stephan, Zhao, Liangyi
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2009
• Subjects: DRNTU::Science::Mathematics::Number theory
• Online Access: https://hdl.handle.net/10356/79584; http://hdl.handle.net/10220/4556; 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
• Institution: Nanyang Technological University

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 ra...