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arXiv · 2007.09819

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

Robson da Silva·James A. Sellers
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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.

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Robson da Silva, James A. Sellers. 2020-07-19. Congruences for the coefficients of the Gordon and McIntosh mock theta function $\xi(q)$. https://arxiv.org/abs/2007.09819

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