q-series and weight 3/2 Maass forms

2009/05/01 by Kathrin Bringmann, Amanda Folsom, Ken Ono · 20 citations
Mathematics · #Advanced Mathematical Identities #Advanced Algebra and Geometry #Analytic Number Theory Research #Mathematics #Modular form #Holomorphic function #Series (stratigraphy) #Pure mathematics #Algebra over a field #Property (philosophy) #Type (biology) #Harmonic #Basic hypergeometric series #Hypergeometric function

paper · pdf · doi:10.1112/s0010437x09004072

published in Compositio Mathematica 145(03), 541-552 (Cambridge University Press)

openalex publication_date 2009/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Abstract Despite the presence of many famous examples, the precise interplay between basic hypergeometric series and modular forms remains a mystery. We consider this problem for canonical spaces of weight 3/2 harmonic Maass forms. Using recent work of Zwegers, we exhibit forms that have the property that their holomorphic parts arise from Lerch-type series, which in turn may be formulated in terms of the Rogers–Fine basic hypergeometric series.

Citations

• Mock Theta Functions
• The f(q) mock theta function conjecture and partition ranks
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• Dyson’s ranks and Maass forms
• On two geometric theta lifts
• Modular forms of weight 1/2
• On Modular Forms of Half Integral Weight

Cited by

• Mock modular form [wikipedia]

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