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

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

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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.

Original languageEnglish (US)
Pages (from-to)62-89
Number of pages28
JournalJournal of Mathematical Analysis and Applications
Volume479
Issue number1
DOIs
StatePublished - Nov 1 2019
Externally publishedYes

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Keywords

  • Congruences
  • Mock theta function
  • Partition

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