Ramanujan congruences for overpartitions with restricted odd differences

Abstract

We investigate Ramanujan congruences for the function which counts the overpartitions of n with restricted odd differences. In particular, we show that only one such congruence exists. Our method involves using the theory of modular forms to prove a more general theorem which bounds the number of primes possible for Ramanujan congruences in certain eta-quotients. This generalizes work done by Jonah Sinick. We also provide two congruences modulo 5 for this function.