The asymptotic formulas for coefficients and algebraicity of Jacobi forms expressed by infinite product

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:471

Article

Jin, Seokho¹  Jo, Sihun² 

[1] Chung Ang Univ, Dept Math, 84 Heukseok Ro, Seoul 06974, South Korea

[2] Woosuk Univ, Dept Math Educ, 443 Samnye Ro, Wanju Gun 55338, Jeollabuk Do, South Korea

关键词: Jacobi forms;    Theta functions;    q-series;   

DOI  :  10.1016/j.jmaa.2018.10.096

来源: Elsevier

【 摘 要 】

We determine asymptotic formulas for the Fourier coefficients of Jacobi forms expressed by infinite products with Jacobi theta functions and the Dedekind eta function. These are generalizations of results about the growth of the Fourier coefficients of Jacobi forms given by an inverse of Jacobi theta function to derive the asymptotic behavior of the Betti numbers of the Hilbert scheme of points on an algebraic surface by Bringmann-Manschot and about the asymptotic behavior of the chi(y)-genera of Hilbert schemes of points on K3 surfaces by Manschot-Rolon. We also get the algebraicity of the generating functions given by Gottsche for the Hilbert schemes associated to general algebraic surfaces. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free