Congruences for the coefficients of the Gordon and McIntosh mock theta function $\xi(q)$

Robson da Silva; James A. Sellers

Congruences for the coefficients of the Gordon and McIntosh mock theta function $\xi(q)$

Number Theory 2024-05-31 v1 Combinatorics

Authors: Robson da Silva , James A. Sellers

Abstract

Recently Gordon and McIntosh introduced the third order mock theta function $\xi(q)$ defined by $\xi(q)=1+2\sum_{n=1}^{\infty}\frac{q^{6n^2-6n+1}}{(q;q^6)_{n}(q^5;q^6)_{n}}.$ Our goal in this paper is to study arithmetic properties of the coefficients of this function. We present a number of such properties, including several infinite families of Ramanujan--like congruences.

Keywords

mock theta function ramanujan congruences arithmetic properties coefficients q-series

Cite

@article{arxiv.2007.09819,
  title  = {Congruences for the coefficients of the Gordon and McIntosh mock theta function $\xi(q)$},
  author = {Robson da Silva and James A. Sellers},
  journal= {arXiv preprint arXiv:2007.09819},
  year   = {2024}
}

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