Two partition functions with congruences modulo 3, 5, 7, and 13

2015/05/24 by Jennings-Shaffer, Chris
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1505.06467

Abstract

We introduce two new integer partition functions, both of which are the number of partition quadruples of n with certain size restrictions. We prove both functions satisfy Ramanujan-type congruences modulo 3, 5, 7, and 13 by use of generalized Lambert series identities and q-series techniques.

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