On Oliver's relations between infinite series and infinite products

K. R. Vasuki; Darshan D.; Ravi G. N

On Oliver's relations between infinite series and infinite products

Number Theory 2026-07-29 v1

Authors: K. R. Vasuki , Darshan D. , Ravi G. N

Abstract

The Jacobi triple product identity provides closed-form expressions for many infinite-product generating functions that arise naturally in combinatorics and number theory. A particularly important application is to Dedekind's eta function {\eta}({\tau}), which it expresses as a theta function. Using the theory of modular forms, Oliver [5] classified all eta quotients that are theta functions. In this paper, we present elementary proofs of the identities established by Oliver.

Keywords

Jacobi triple product eta quotients theta functions modular forms infinite products infinite series

Cite

@article{arxiv.2607.26471,
  title  = {On Oliver's relations between infinite series and infinite products},
  author = {K. R. Vasuki and Darshan D. and Ravi G. N},
  journal= {arXiv preprint arXiv:2607.26471},
  year   = {2026}
}

Comments

16 pages, submitted