Efficient computation of the overpartition function and applications

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.

arXiv commentFinal version, published in Journal of Mathematical Analysis and Applications

References in corpus (4)

• Rank and crank moments for overpartitions
• Rank differences for overpartitions
• Efficient implementation of the Hardy-Ramanujan-Rademacher formula
• Congruences satisfied by eta-quotients

Cited by in corpus (1)

• Explicit families of congruences for the overpartition function