Congruences modulo powers of 11 for some eta-quotients

被引：2

作者：

Petta Mestrige, Shashika ^{[1
]}

机构：

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

来源：

RESEARCH IN NUMBER THEORY | 2019年 / 6卷 / 01期

关键词：

CUBIC CONTINUED-FRACTION;

D O I：

10.1007/s40993-019-0180-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The partition function p([1c11d])(n) can be defined using the generating function, Sigma(infinity)(n=0) p([1c11d])(n)q(n) = Pi(infinity)(n=1) 1/(1 - q(n))(c)(1 - q(11n))(d). In this paper, we prove infinite families of congruences for the partition function p([1c11d])(n) modulo powers of 11 for any integers c and d, which generalizes Atkin and Gordon's congruences for powers of the partition function. The proofs use an explicit basis for the vector space of modular functions of the congruence subgroup Gamma(0)(11).

引用

页数：10