Stark conjectures for CM elliptic curves over number fields

被引：2

作者：

Stopple, J ^{[1
]}

机构：

[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

来源：

JOURNAL OF NUMBER THEORY | 2003年 / 103卷 / 02期

关键词：

Stark conjectures; Beilinson conjectures; special values of L-functions;

D O I：

10.1016/S0022-314X(03)00112-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present an elliptic curve analog of the Stark conjecture for the value of the L-function at s = 0. Although implied by the general Beilinson conjectures, the approach here is very concrete. Several cases are proved. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：163 / 196

页数：34

共 50 条

[31] PRIME NUMBER RACES FOR ELLIPTIC CURVES OVER FUNCTION FIELDS
Cha, Byungchul
Fiorilli, Daniel
Jouve, Florent
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2016, 49 (05): : 1239 - 1277
[32] Bounds for torsion points on elliptic curves over number fields
Merel, L
INVENTIONES MATHEMATICAE, 1996, 124 (1-3) : 437 - 449
[33] Torsion Groups of a Family of Elliptic Curves Over Number Fields
Dey, Pallab Kanti
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2019, 69 (01) : 161 - 171
[34] The Tamagawa number conjecture for CM elliptic curves
Kings, G
INVENTIONES MATHEMATICAE, 2001, 143 (03) : 571 - 627
[35] The Tamagawa number conjecture for CM elliptic curves
Guido Kings
Inventiones mathematicae, 2001, 143 : 571 - 627
[36] A lower bound on the proportion of modular elliptic curves over Galois CM fields
Feng, Zachary
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2024, 20 (02) : 481 - 486
[37] Stark-Heegner points on elliptic curves defined over imaginary quadratic fields
Trifkovic, Mak
DUKE MATHEMATICAL JOURNAL, 2006, 135 (03) : 415 - 453
[38] Infinite families of elliptic curves over Dihedral quartic number fields
Jeon, Daeyeol
Kim, Chang Heon
Lee, Yoonjin
JOURNAL OF NUMBER THEORY, 2013, 133 (01) : 115 - 122
[39] Cryptography on elliptic curves over p-adic number fields
MaoZhi Xu
ChunLai Zhao
Min Feng
ZhaoRong Ren
JiQing Ye
Science in China Series F: Information Sciences, 2008, 51 : 258 - 272
[40] Reduction of elliptic curves over certain real quadratic number fields
Kida, M
MATHEMATICS OF COMPUTATION, 1999, 68 (228) : 1679 - 1685

← 1 2 3 4 5 →