On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras

2019/10/31 by Lea Beneish, Michael H. Mertens
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Dimension (graph theory) #Discrete mathematics #Graph #Hecke operator #Holomorphic function #Jordan algebra #Mathematics #Modular design #Modular form #Nonlinear Waves and Solitons #Operator (biology) #Operator algebra #Pure mathematics #Vertex (graph theory) #Vertex operator algebra #math.NT #math.QA #math.RT #msc:11F03 #msc:11F22 #msc:17B69

paper · pdf · doi:10.1007/s00209-020-02499-4

v3: 28 pages, some minor typos fixed, incorporating referee's comments. Final version accepted for publication

arxiv created 2020/02/06 · openalex publication_date 2020/03/02 · arxiv updated 2020/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract Using techniques from the theory of mock modular forms and harmonic Maaß forms, especially Weierstrass mock modular forms, we establish several dimension formulas for certain holomorphic, strongly rational vertex operator algebras, complementing previous work by van Ekeren, Möller, and Scheithauer.

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