Arithmetic properties of the Fourier coefficients of the eighth-order mock theta function

Arooj Fatima; Fatemah Mofarreh; Ahmer Ali; Arooj Fatima; Fatemah Mofarreh; Ahmer Ali

doi:10.3934/math.2026569

AIMS Mathematics

2026, Volume 11, Issue 5: 13818-13836. doi: 10.3934/math.2026569

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Arithmetic properties of the Fourier coefficients of the eighth-order mock theta function

1.
Department of Mathematics, Government College Women University, Sialkot 51300, Pakistan
2.
Mathematical Science Department, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11546, Saudi Arabia
3.
Department of Mathematics, University of Narowal, Narowal 51600, Pakistan

Received: 17 March 2026 Revised: 07 May 2026 Accepted: 11 May 2026 Published: 18 May 2026
MSC : Primary 11F27; Secondary 11F37, 05A17

In this paper, we investigate the arithmetic properties of the coefficients of the eighth-order mock theta function $ V_0 (q) $, building upon the foundational work of Gordon and McIntosh on mock theta functions. Several novel dissection formulas are derived, leading to new identities for the Dedekind eta function at level 8. Furthermore, we establish new congruence relations and partition recurrence formulas associated with the coefficients of the eighth-order mock theta function.
- mock theta function,
- $ q $-series,
- congruence relation,
- Jacobi triple product,
- modular forms,
- Eisenstein series,
- cusp forms,
- integer partition
Citation: Arooj Fatima, Fatemah Mofarreh, Ahmer Ali. Arithmetic properties of the Fourier coefficients of the eighth-order mock theta function[J]. AIMS Mathematics, 2026, 11(5): 13818-13836. doi: 10.3934/math.2026569

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Abstract

In this paper, we investigate the arithmetic properties of the coefficients of the eighth-order mock theta function $ V_0 (q) $, building upon the foundational work of Gordon and McIntosh on mock theta functions. Several novel dissection formulas are derived, leading to new identities for the Dedekind eta function at level 8. Furthermore, we establish new congruence relations and partition recurrence formulas associated with the coefficients of the eighth-order mock theta function.

References

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