2019/06/25 by Haowu Wang, Wang, Haowu · 2 citations
Mathematics · #11F50 #11F55 #14J28 #51F15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Primary 11F03 #Secondary 17B67
paper · pdf · doi:10.48550/arxiv.1906.10459
openalex publication_date 2019/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classification of reflective modular forms is an important problem in the theory of automorphic forms on orthogonal groups. In this paper, we develop an approach based on the theory of Jacobi forms to give a full classification of 2-reflective modular forms. We prove that there are only 3 lattices of signature (2,n) having 2-reflective modular forms when n≥ 14. We show that there are exactly 51 lattices of type 2U⊕ L(-1) which admit 2-reflective modular forms and satisfy that L has 2-roots. We further determine all 2-reflective modular forms giving arithmetic hyperbolic 2-reflection groups. This is the first attempt to classify reflective modular forms on lattices of arbitrary level.