The Darmon-Dasgupta units over genus fields and the Shimura correspondence

被引：2

作者：

Park, Jeehoon ^{[1
]}

机构：

[1] McGill Univ, Dept Math, Montreal, PQ H3A 2K6, Canada

来源：

JOURNAL OF NUMBER THEORY | 2010年 / 130卷 / 11期

关键词：

Elliptic units for real quadratic fields; Gross-Stark conjecture; Genus fields; STARK-HEEGNER POINTS; MODULAR-FORMS; NEGATIVE INTEGERS; ELLIPTIC UNITS; VALUES; SUMS;

D O I：

10.1016/j.jnt.2010.05.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a special case of the Gross-Stark conjecture (Gross. 1981 [Gr]), namely over genus fields. Based on the same idea we provide evidence of the rationality conjecture of the elliptic units for real quadratic fields over genus fields, which is a refinement of the Gross-Stark conjecture given by Darmon and Dasgupta (2006) [DO]. Then a relationship between these units and the Fourier coefficients of p-adic Eisenstein series of half-integral weight is explained. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2610 / 2627

页数：18

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