2013/09/19 by Henry H. Kim, Kyu-Hwan Lee, Kyu‐Hwan Lee +4
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT
paper · pdf · doi:10.48550/arxiv.1309.5095
arxiv created 2013/09/19 · openalex publication_date 2013/09/19 · arxiv updated 2013/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we compute basis elements of certain spaces of weight 0 weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. We use the results to construct automorphic correction of the rank 2 hyperbolic Kac-Moody algebras H(a), a=4,5,6, through Hilbert modular forms explicitly given by Borcherds lifts of the weakly holomorphic modular forms. We also compute asymptotic of the Fourier coefficients as they are related to root multiplicities of the rank 2 hyperbolic Kac-Moody algebras. This work is a continuation of the previous paper, where automorphic correction was constructed for H(a), a=3, 11, 66.