An infinite family of congruences arising from a second order mock theta function

Shane Chern; Chun Wang

An infinite family of congruences arising from a second order mock theta function

Number Theory 2018-03-07 v1

Authors: Shane Chern , Chun Wang

Abstract

Let $\beta(q)=\sum_{n\ge 0} \mathfrak{b}(n)q^n$ be a second order mock theta function defined by $\sum_{n\ge 0}\frac{q^{n(n+1)}(-q^2;q^2)_n}{(q;q^2)_{n+1}^2}.$ In this paper, we obtain an infinite family of congruences modulo powers of $3$ for $\mathfrak{b}(n)$ .

Keywords

mock theta function congruences modular powers second order

Cite

@article{arxiv.1803.01976,
  title  = {An infinite family of congruences arising from a second order mock theta function},
  author = {Shane Chern and Chun Wang},
  journal= {arXiv preprint arXiv:1803.01976},
  year   = {2018}
}

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