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 & Statistics

Research output: Contribution to journal › Article › peer-review

23 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

Bibliographical note

Funding Information:
The second author was supported by FAPESP (grant no. 2016/14057-2 ).

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Congruences
Mock theta function
Partition

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10.1016/j.jmaa.2019.06.016

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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.",

keywords = "Congruences, Mock theta function, Partition",

author = "Brietzke, \{Eduardo H.M.\} and \{da Silva\}, Robson and Sellers, \{James A.\}",

note = "Funding Information: The second author was supported by FAPESP (grant no. 2016/14057-2 ). Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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AU - da Silva, Robson

AU - Sellers, James A.

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N2 - 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.

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.

KW - Congruences

KW - Mock theta function

KW - Partition

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IS - 1

ER -

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

Abstract

Bibliographical note

Keywords

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