Reciprocals of false theta functions
Combinatorics
2025-08-05 v2
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 and the truncated pentagonal number theorem of Andrews and Merca. We record a useful dissection identity analogous to the known theta function dissection.
Cite
@article{arxiv.2412.19998,
title = {Reciprocals of false theta functions},
author = {William J. Keith},
journal= {arXiv preprint arXiv:2412.19998},
year = {2025}
}
Comments
Submitted for Proceedings of the Legacy of Ramanujan Conference 2024, in honor of the 85th birthdays of George Andrews and Bruce Berndt. v2: Minor typographical corrections and changes made from reader comments. No mathematical change