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On Oliver's relations between infinite series and infinite products

2026/07/29 by K. R. Vasuki, Darshan D., Ravi G. N
Mathematics · #math.NT #msc:11F20 #msc:11F27

paper · pdf

16 pages, submitted

arxiv created 2026/07/29 · arxiv updated 2026/07/30

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 η(τ), 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.

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