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June 5, 2026International Journal of Number Theory0 citations

New congruences for the mock theta function ψ_ (q)

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JJJing JinHXH. XuOYOlivia X. M. Yao

Key Points

  • This research aims to explore congruence properties of the sixth order mock theta function ψ(q).
  • Demonstrated congruences modulo 3 and 4 for the mock theta function ψ(q) defined by Berndt and Chan.
  • Built on previous findings regarding congruences and coefficients of mock theta functions.
  • Introduced several new congruences for coefficients of the sixth order mock theta function.
  • Expanded upon existing knowledge of congruences modulo 4 established by Chen and Garvan.

Abstract

In recent years, congruence properties for the coefficients of mock theta functions have received a lot of attention. In 2021, Wang gave a systematic study on the parity of coefficients of classical mock theta functions. Recently, Chen and Garvan proved a number of congruences modulo 4 for five mock theta functions. In this paper, we show several congruences modulo 3 and 4 for the sixth order mock theta function ψ_ (q) defined by Berndt and Chan.

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Cite This Study

Jin et al. (2026) studied this question.

synapsesocial.com/papers/6a22692e763171746d547bfchttps://doi.org/10.1142/s1793042126501125
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