The Beilinson conjectures for CM elliptic curves via hypergeometric functions

被引：4

作者：

Ito, Ryojun ^{[1
]}

机构：

[1] Chiba Univ, Grad Sch Sci, Dept Math & Informat, Inage Ku, Yayoicho 1-33, Chiba 2638522, Japan

来源：

RAMANUJAN JOURNAL | 2018年 / 45卷 / 02期

关键词：

L-value of elliptic curve; Regulator; Beilinson conjectures; Hypergeometric function; HECKE L-FUNCTIONS; FERMAT-CURVES; VALUES;

D O I：

10.1007/s11139-016-9859-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider certain CM elliptic curves which are related to Fermat curves, and express the values of L-functions at in terms of special values of generalized hypergeometric functions. We compare them and a similar result of Rogers-Zudilin with Otsubo's regulator formulas, and give a new proof of the Beilinson conjectures originally due to Bloch.

引用

页码：433 / 449

页数：17

共 35 条

[1] The Beilinson conjectures for CM elliptic curves via hypergeometric functions
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The Ramanujan Journal, 2018, 45 : 433 - 449
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[9] A numerical approach toward the p-adic Beilinson conjecture for elliptic curves over Q
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[10] FUNCTIONAL INEQUALITIES FOR HYPERGEOMETRIC-FUNCTIONS AND COMPLETE ELLIPTIC INTEGRALS
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