Congruences related to an eighth order mock theta function of Gordon and McIntosh

Eduardo H.M. Brietzke; Robson da Silva; James A. Sellers

doi:10.1016/j.jmaa.2019.06.016

Congruences related to an eighth order mock theta function of Gordon and McIntosh

Eduardo H.M. Brietzke, Robson da Silva, James A. Sellers

Mathematics

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14 Scopus citations

Abstract

In this paper, we study arithmetic properties of a partition function related to an eighth order mock theta function of Gordon and McIntosh. Via elementary generating function manipulations, a complete characterization of the parity of this function is presented, from which infinitely many Ramanujan-like congruences modulo 2 are obtained. In addition, many congruences modulo certain numbers of the form 2^α3^β5 are presented.

Original language	English (US)
Pages (from-to)	62-89
Number of pages	28
Journal	Journal of Mathematical Analysis and Applications
Volume	479
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2019.06.016
State	Published - Nov 1 2019

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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abstract = "In this paper, we study arithmetic properties of a partition function related to an eighth order mock theta function of Gordon and McIntosh. Via elementary generating function manipulations, a complete characterization of the parity of this function is presented, from which infinitely many Ramanujan-like congruences modulo 2 are obtained. In addition, many congruences modulo certain numbers of the form 2α3β5 are presented.",

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AB - In this paper, we study arithmetic properties of a partition function related to an eighth order mock theta function of Gordon and McIntosh. Via elementary generating function manipulations, a complete characterization of the parity of this function is presented, from which infinitely many Ramanujan-like congruences modulo 2 are obtained. In addition, many congruences modulo certain numbers of the form 2α3β5 are presented.

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Congruences related to an eighth order mock theta function of Gordon and McIntosh

Abstract

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