Proof of a conjecture of Keith on congruences of the reciprocal of a false theta function

2025/08/03 by Jing Jin, Sijia Wang, Jin, Jing +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2508.01532

openalex publication_date 2025/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Keith investigated reciprocals of false theta functions and proved some interesting results such as congruences, asymptotic bounds, and combinatorial identities. At the end of his paper, Keith posed a conjecture on congruences modulo 4 and 8 for the coefficients of the reciprocal of a false theta function. In this paper, we not only confirm Keith's conjecture, but also prove a generalized result.

Citations

• Reciprocals of false theta functions
• New Proofs of Ramanujan's Identities on False Theta Functions
• Explicit Formulas for Partition Pairs and Triples with 3-Cores

Related

• Parity results for the reciprocals of false theta functions
• Reciprocals of false theta functions
• Congruence properties of coefficients of the eighth order mock theta function V₀(q)
• On certain explicit congruences for mock theta functions
• New Proofs of Ramanujan's Identities on False Theta Functions