More congruences for the coefficients of quotients of Eisenstein series

被引：2

作者：

Mahlburg, K ^{[1
]}

机构：

[1] Dept Math, Madison, WI 53706 USA

来源：

JOURNAL OF NUMBER THEORY | 2005年 / 115卷 / 01期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/j.jnt.2004.10.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Berndt and Yee (Acta Arith. 104 (2002) 297) recently proved congruences for the coefficients of certain quotients of Eisenstein series. In each case, they showed that an arithmetic progression of coefficients is identically zero modulo a small power of 3 or 7. The present paper extends these results by proving that there are infinite classes of odd primes for which the set of coefficients that are zero modulo an arbitrary prime power is a set of arithmetic density one. A new family of explicit congruences modulo arbitrary powers of 2 is also found. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：89 / 99

页数：11

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