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.
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收藏
页码：865 / 879
页数：15
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