Congruence properties of coefficients of the eighth order mock theta function $V_0(q)$

TL;DR

This paper investigates divisibility and congruence properties of coefficients related to the eighth order mock theta function V_0(q), revealing new congruences modulo powers of 2 and other primes, similar to classical partition congruences.

Contribution

It establishes new divisibility properties and infinite families of congruences for coefficients of the mock theta function V_0(q), extending Ramanujan-like results.

Findings

Congruences modulo powers of 2 for certain coefficients.

Infinite families of congruences modulo 13, 25, and 27.

New divisibility properties of the associated partition function.

Abstract

We study the divisibility properties of the partition function associated with the eighth order mock theta function $V_0(q)$, introduced by Gordon and McIntosh. We obtain congruences modulo powers of 2 for certain coefficients of the partition function, akin to Ramanujan's partition congruences. Further, we also present several infinite families of congruences molulo 13, 25 and 27.