Ramanujan congruences for overpartitions with restricted odd differences

Michael Hanson; Jeremiah Smith

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arXiv · 2204.02444

Ramanujan congruences for overpartitions with restricted odd differences

Michael Hanson·Jeremiah Smith

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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.

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Michael Hanson, Jeremiah Smith. 2022-04-05. Ramanujan congruences for overpartitions with restricted odd differences. https://arxiv.org/abs/2204.02444

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