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arXiv · 2412.19998

Reciprocals of false theta functions

William J. Keith
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Abstract

We investigate reciprocals of false theta functions, producing results such as congruences, simple asymptotic bounds, and combinatorial identities. Of particular interest is a connection between $1/Ψ(-q^2,q)$ and the truncated pentagonal number theorem of Andrews and Merca. We record a useful dissection identity analogous to the known theta function dissection.

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William J. Keith. 2025-01-04. Reciprocals of false theta functions. https://doi.org/10.1007/s11139-025-01179-3

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