Reciprocals of false theta functions

2024/12/28 by Keith, William J. · 2 citations
#05A17 #11F27 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.19998

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(-q²,q) and the truncated pentagonal number theorem of Andrews and Merca. We record a useful dissection identity analogous to the known theta function dissection.

Cited by

• Parity results for the reciprocals of false theta functions
• Proof of a conjecture of Keith on congruences of the reciprocal of a false theta function

Related

• Proof of a conjecture of Keith on congruences of the reciprocal of a false theta function
• Parity results for the reciprocals of false theta functions
• Some Identities associated with mock theta functions ω(q) and ν(q)
• Further q-series identities and conjectures relating false theta\n functions and characters
• New Proofs of Ramanujan's Identities on False Theta Functions