On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramanujan's ω(q)

2016/12/24 by Kathrin Bringmann, Bringmann, Kathrin, Chris Jennings-Shaffer +3
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1612.08219

openalex publication_date 2016/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the mock modular behavior of P_ω(q), a partition function introduced by Andrews, Dixit, Schultz, and Yee. This function arose in a study of smallest parts functions related to classical third order mock theta functions, one of which is ω(q). We find that the modular completion of P_ω(q) is not simply a harmonic Maass form, but is instead the derivative of a linear combination of products of various harmonic Maass forms and theta functions. We precisely describe its behavior under modular transformations and find that the image under the Maass lowering operator lies in a relatively simpler space.

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