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arXiv · 1707.04627

Lacunary Eta-quotients Modulo Powers of Primes

Tessa Cotron·Anya Michaelsen·Emily Stamm·Weitao Zhu
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Abstract

An integral power series is called lacunary modulo $M$ if almost all of its coefficients are divisible by $M$. Motivated by the parity problem for the partition function, $p(n)$, Gordon and Ono studied the generating functions for $t$-regular partitions, and determined conditions for when these functions are lacunary modulo powers of primes. We generalize their results in a number of ways by studying infinite products called Dedekind eta-quotients and generalized Dedekind eta-quotients. We then apply our results to the generating functions for the partition functions considered by Nekrasov, Okounkov, and Han.

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Tessa Cotron, Anya Michaelsen, Emily Stamm, Weitao Zhu. 2019-01-10. Lacunary Eta-quotients Modulo Powers of Primes. https://arxiv.org/abs/1707.04627

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