Families of Congruences for Fractional Partition Functions Modulo Powers of Primes

TL;DR

This paper discovers new families of congruences modulo prime powers for fractional partition functions and extends these results to 2-color partition functions, building on prior work by Chan and Wang.

Contribution

It introduces novel families of congruences for fractional partition functions modulo prime powers and extends these to 2-color partition functions.

Findings

New congruences modulo prime powers for fractional partition functions

Analogous congruences for 2-color partition functions

Extension of previous results by Chan and Wang

Abstract

Recently, Chan and Wang (Fractional powers of the generating function for the partition function. Acta Arith. 187(1), 59--80 (2019)) studied the fractional powers of the generating function for the partition function and found several congruences satisfied by the corresponding coefficients. In this paper, we find some new families of congruences modulo powers of primes. We also find analogous results for the coefficients of the fractional powers of the generating function for the 2-color partition function.