Parity results for the reciprocals of false theta functions
Jing Jin, Huan Xu, Olivia X.M. Yao
TL;DR
This paper proves new parity results for the reciprocals of false theta functions using Ramanujan's theta identities, confirming some of Keith's conjectures on their arithmetic properties.
Contribution
It introduces novel parity results for reciprocals of false theta functions, advancing understanding of their arithmetic nature and resolving some of Keith's conjectures.
Findings
Parity results for reciprocals of false theta functions
Confirmation of Keith's conjectures on these functions
Use of Ramanujan's theta identities in proofs
Abstract
Recently, Keith investigated arithmetic properties for the reciprocals of some false theta functions and posed several conjectures. In this paper, we prove some parity results for the reciprocals of some false theta functions by using some identities on Ramanujan's general theta function. In particular, our results imply some conjectures of Keith.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics