Recently Gordon and McIntosh introduced the third order mock theta function ξ(q) defined by ξ(q)=1+2∑n=1∞q6n2-6n+1(q;q6)n(q5;q6)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.
Bibliographical noteFunding Information:
Robson da Silva was supported by São Paulo Research Foundation (FAPESP) (Grant No. 2019/14796-8)
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Generating function
- Mock theta function