|DATE||April 20 (Fri), 2018|
|TITLE||The asymptotic formulas for coefficients and algebraicity of Jacobi forms expressed by infinite product|
|ABSTRACT||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-
Manshot and about the asymptotic behavior of the \chi_y -genera of Hilbert schemes of points
on K3 surfaces by Msnshot-Rolon.
And we get the algebraicity of the generating functions given by G?ttsche for the Hilbert
schemes associated to general algebraic surfaces.