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arXiv · 1601.05287

Extension of a proof of the Ramanujan congruences for multipartitions

Oleg Lazarev·Matthew S. Mizuhara·Benjamin Reid·Holly Swisher
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Abstract

Recently Lachterman, Schayer, and Younger published an elegant proof of the Ramanujan congruences for the partition function $p(n)$. Their proof uses only the classical theory of modular forms as well as a beautiful result of Choie, Kohnen, and Ono, without need for Hecke operators. In this paper we give a method for generalizing Lachterman, Schayer, and Younger's proof to include Ramanujan congruences for multipartition functions $p_k(n)$, and Ramanujan congruences for $p(n)$ modulo certain prime powers.

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Oleg Lazarev, Matthew S. Mizuhara, Benjamin Reid, Holly Swisher. 2016-01-20. Extension of a proof of the Ramanujan congruences for multipartitions. https://arxiv.org/abs/1601.05287

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