| ชื่อเรื่อง | : | On the low-lying zeros of Hasse–Weil L-functions for elliptic curves |
| นักวิจัย | : | Baier, Stephan , Zhao, Liangyi |
| คำค้น | : | DRNTU::Science::Mathematics::Number theory |
| หน่วยงาน | : | Nanyang Technological University, Singapore |
| ผู้ร่วมงาน | : | - |
| ปีพิมพ์ | : | 2551 |
| อ้างอิง | : | 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. , 0001-8708 , 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 , 132885 |
| ที่มา | : | - |
| ความเชี่ยวชาญ | : | - |
| ความสัมพันธ์ | : | Advances in Mathematics. |
| ขอบเขตของเนื้อหา | : | - |
| บทคัดย่อ/คำอธิบาย | : | 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. |
| บรรณานุกรม | : |
Baier, Stephan , Zhao, Liangyi . (2551). On the low-lying zeros of Hasse–Weil L-functions for elliptic curves.
กรุงเทพมหานคร : Nanyang Technological University, Singapore. Baier, Stephan , Zhao, Liangyi . 2551. "On the low-lying zeros of Hasse–Weil L-functions for elliptic curves".
กรุงเทพมหานคร : Nanyang Technological University, Singapore. Baier, Stephan , Zhao, Liangyi . "On the low-lying zeros of Hasse–Weil L-functions for elliptic curves."
กรุงเทพมหานคร : Nanyang Technological University, Singapore, 2551. Print. Baier, Stephan , Zhao, Liangyi . On the low-lying zeros of Hasse–Weil L-functions for elliptic curves. กรุงเทพมหานคร : Nanyang Technological University, Singapore; 2551.
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