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FIELD Mathematics April 20 (Fri), 2018 17:00-18:00 1424 Seok-Ho Jin Kim, Seungki Áß¾Ó´ëÇÐ±³ The asymptotic formulas for coefficients and algebraicity of Jacobi forms expressed by infinite product We determine asymptotic formulas for the Fourier coefficients of Jacobi formsexpressed 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 Jacobiforms given by an inverse of Jacobi theta function to derive the asymptotic behavior ofthe 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 pointson K3 surfaces by Msnshot-Rolon.And we get the algebraicity of the generating functions given by G?ttsche for the Hilbertschemes associated to general algebraic surfaces.

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