This article is cited in 7 papers

Papers published in the English version of the journal

Some Congruences for Overpartitions with Restriction

H. M. Srivastava^abc, N. Saikia<sup>d

a</sup> Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3R4, Canada
^b Department of Medical Research, China Medical University, Taichung, Taiwan, 40402, Republic of China
^c Department of Mathematics and Informatics, Azerbaijan University, Baku, AZ1007, Azerbaijan
^d Department of Mathematics, Rajiv Gandhi University, Doimukh, Arunachal Pradesh, 791112, India

Abstract: For any given positive integers $m$ and $n$, let $\overline{p}_m(n)$ denote the number of overpartitions of $n$ with no parts divisible by $4m$ and only the parts congruent to $m$ modulo $2m$ overlined. In this paper, we prove Ramanujan-type congruences modulo 2 for $\overline{p}_m(n)$ by applying $q$-series and Ramanujan's theta-function identities.

Keywords: congruences, partitions, generating functions, overpartitions with restriction, theta-function identities.

Received: 02.12.2019

Language: English

 English version: Mathematical Notes, 2020, 107:3, 488–498

Bibliographic databases:

• 
• 
• 
•