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

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 thet...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 471; no. 1-2; pp. 623 - 646
Main Authors Jin, Seokho, Jo, Sihun
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2019
Subjects
Jacobi forms
q-series
Theta functions
q-series
Theta functions
Jacobi forms
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Summary: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 χy-genera of Hilbert schemes of points on K3 surfaces by Manschot–Rolon. We also get the algebraicity of the generating functions given by Göttsche for the Hilbert schemes associated to general algebraic surfaces.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.10.096