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arXiv · 2508.01532

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

Jing Jin·Sijia Wang·Olivia X. M. Yao
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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.

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Jing Jin, Sijia Wang, Olivia X. M. Yao. 2025-08-03. Proof of a conjecture of Keith on congruences of the reciprocal of a false theta function. https://arxiv.org/abs/2508.01532

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