Ramanujan congruences for overpartitions with restricted odd differences

2022/04/05 by Hanson, Michael, Smith, Jeremiah · 1 citation
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paper · doi:10.48550/arxiv.2204.02444

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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• Block-Separated Overpartitions: Fibonacci Structure and Euler Factorization

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