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arXiv · 2309.00302

Arithmetic properties of overpartitions

Qi-Yang Zheng
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Abstract

The primary focus of this paper is overpartitions, a type of partition that plays a significant role in $q$-series theory. In 2006, Treneer discovered an explicit infinite family of congruences of overpartitions modulo $5$. In our research, we have identified explicit infinite families of congruences of overpartitions modulo $3,7,11$. This work reveals the connection between overpartitions and half-integral modular forms.

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Qi-Yang Zheng. 2023-09-01. Arithmetic properties of overpartitions. https://arxiv.org/abs/2309.00302

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