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arXiv · 2303.15895

Efficient computation of the overpartition function and applications

Adrian Barquero-Sanchez·Gabriel Collado-Valverde·Nathan C. Ryan·Eduardo Salas-Jimenez·Nicolás Sirolli·Jean Carlos Villegas-Morales
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Abstract

In this paper we develop a method to calculate the overpartition function efficiently using a Hardy-Rademacher-Ramanujan type formula, and we use this method to find many new Ramanujan-style congruences, whose existence is predicted by Treneer and a few of which were first discovered by Ryan, Scherr, Sirolli and Treneer.

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Adrian Barquero-Sanchez, Gabriel Collado-Valverde, Nathan C. Ryan, Eduardo Salas-Jimenez, Nicolás Sirolli, Jean Carlos Villegas-Morales. 2023-03-28. Efficient computation of the overpartition function and applications. https://doi.org/10.1016/j.jmaa.2023.127472

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