Abstract
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.
Original language | English (US) |
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Pages (from-to) | 815-834 |
Number of pages | 20 |
Journal | Ramanujan Journal |
Volume | 58 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2022 |
Bibliographical note
Funding Information:Robson da Silva was supported by São Paulo Research Foundation (FAPESP) (Grant No. 2019/14796-8)
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Congruence
- Generating function
- Mock theta function