Bailey pairs and quantum $q$-series identites. I. The classical identities
Number Theory
2025-09-26 v1 Classical Analysis and ODEs
Combinatorics
Abstract
We use Bailey pairs to prove -series identities at roots of unity due to Cohen and Bryson-Ono-Pitman-Rhoades. The proofs use Bailey pairs with quadratic forms developed in the study of mock theta functions. In addition to the standard Bailey lemma, we require some changes-of-base established by Bressoud-Ismail-Stanton. We then embed the identities in infinite families using the Bailey chain.
Cite
@article{arxiv.2509.21230,
title = {Bailey pairs and quantum $q$-series identites. I. The classical identities},
author = {Jehanne Dousse and Jeremy Lovejoy},
journal= {arXiv preprint arXiv:2509.21230},
year = {2025}
}
Comments
15 pages