A REFINEMENT OF RAMANUJAN'S CONGRUENCES MODULO POWERS OF 7 AND 11

被引：1

作者：

Jameson, Marie ^{[1
]}

机构：

[1] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2012年 / 8卷 / 04期

关键词：

Partition function; Ramanujan congruences; Hecke eigenforms; elliptic curves; PARTITION-FUNCTION;

D O I：

10.1142/S1793042112500510

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Ramanujan's famous congruences for the partition function modulo powers of 5, 7, and 11 have inspired much further research. For example, in 2002 Lovejoy and Ono found subprogressions of 5(j)n + beta(5)(j) for which Ramanujan's congruence mod 5(j) could be strengthened to a statement modulo 5(j+1). Here we provide the analogous results modulo powers of 7 and 11. We require the arithmetic properties of two special elliptic curves.

引用

页码：865 / 879

页数：15

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