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April 2020 Congruences for $\ell$-regular partitions and bipartitions
Su-Ping Cui, Nancy S. S. Gu
Rocky Mountain J. Math. 50(2): 513-526 (April 2020). DOI: 10.1216/rmj.2020.50.513

Abstract

Define F ( q ) : = n = ( 1 ) δ n ( a n + b ) q ( c n 2 + d n ) 2 , which includes Ramanujan’s theta function as a special case. We establish a dissection identity for this function, and use it to derive congruence properties for the coefficients of F ( q ) . As an application we deduce several infinite families of congruences for -regular partitions and -regular bipartitions. In addition, we give a new proof of Ramanujan’s congruence for the unrestricted partition function modulo 5 .

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Su-Ping Cui. Nancy S. S. Gu. "Congruences for $\ell$-regular partitions and bipartitions." Rocky Mountain J. Math. 50 (2) 513 - 526, April 2020. https://doi.org/10.1216/rmj.2020.50.513

Information

Received: 26 July 2019; Revised: 29 September 2019; Accepted: 30 September 2019; Published: April 2020
First available in Project Euclid: 29 May 2020

zbMATH: 07210975
MathSciNet: MR4104390
Digital Object Identifier: 10.1216/rmj.2020.50.513

Subjects:
Primary: 11P83
Secondary: 05A17

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 2 • April 2020
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