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Overpartition function modulo $16$ and some binary quadratic forms

Xinhua Xiong

Xinhua Xiong

Department of Mathematics, China Three Gorges University, Yichang, Hubei Province 443002, P. R. China

E-mail Address: xinhuaxiong@ctgu.edu.cn

E-mail Address: xinhuaxiong@yahoo.com

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https://doi.org/10.1142/S1793042116500731Cited by:6 (Source: Crossref)

Abstract

Let $\bar{p} (n)$ denote the number of overpartitions of $n$ . In this paper, we will give a complete determination of $\bar{p} (n)$ modulo $16$ by relating it to some binary quadratic forms; this will generalize the result of Kim on $\bar{p} (n)$ modulo $8$ . Moreover, we give infinitely many new Ramanujan-like congruences for overpartition function modulo $16$ .

Keywords:

AMSC: 11P83

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