Class numbers of real quadratic fields

被引：1

作者：

Byeon, Dongho ^{[1
]}

Kim, Jigu ^{[2
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul, South Korea

[2] Ewha Womans Univ, Inst Math Sci, Seoul, South Korea

来源：

JOURNAL OF NUMBER THEORY | 2022年 / 231卷

基金：

新加坡国家研究基金会;

关键词：

Class number; Real quadratic fields; L-function; Elliptic curve; SPECIAL VALUES;

D O I：

10.1016/j.jnt.2020.11.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let d > 0 be a fundamental discriminant of a real quadratic field. Let h(d) be the class number and epsilon(d) the fundamental unit of the real quadratic field Q(root d). In this paper, we prove that if there is an elliptic curve E over Q whose Hasse-Weil L-function L-E/Q(S) has a zero of order g at s = 1, then there is an effectively computable constant k > 0 satisfying h(d) log epsilon(d) > 1/k (log d)(g-3) Pi(p vertical bar d, p not equal d) (1-left perpendicular2 root p right perpendicular/p+1). (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：1 / 47

页数：47

共 19 条

[1] An explicit lower bound for special values of Dirichlet L-functions II [J].