Overpartition function modulo 16 and some binary quadratic forms-Reference-Cited by-同舟云学术

Overpartition function modulo 16 and some binary quadratic forms

Published:2016-05-10 Issue:05 Volume:12 Page:1195-1208
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Xiong Xinhua¹

Affiliation:

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

Abstract

Let [Formula: see text] denote the number of overpartitions of [Formula: see text]. In this paper, we will give a complete determination of [Formula: see text] modulo [Formula: see text] by relating it to some binary quadratic forms; this will generalize the result of Kim on [Formula: see text] modulo [Formula: see text]. Moreover, we give infinitely many new Ramanujan-like congruences for overpartition function modulo [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042116500731

Reference11 articles.

1. Proof of a conjecture of Hirschhorn and Sellers on overpartitions

2. Weakly holomorphic modular forms of half-integral weight with nonvanishing constant terms modulo $\ell $

3. Overpartitions

4. Jagged Partitions

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