Mock theta functions and indefinite modular forms

2022/06/06 by Minoru Wakimoto, Wakimoto, Minoru
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2206.02293

openalex publication_date 2022/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the explicit formula for the signed mock theta functions Φ^(-)[m,s] obtained from the coroot lattice of D(2,1;a), functions with indefinite quadratic forms naturally take place. We compute their modular transformation properties by applying the Zwegers' modification theory of mock theta functions and show that the C-linear span of these functions is SL₂(Z)-invariant.

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