an:06441797
Zbl 1370.11056
Meher, Jaban; Shankhadhar, Karam Deo
Asymptotic formulas for the coefficients of certain automorphic functions
EN
Acta Arith. 169, No. 1, 59-76 (2015).
00344667
2015
j
11F30 11F50 11F03
asymptotic formula; Fourier coefficients; weakly holomorphic modular forms; Jacobi-Eisenstein series; weak Jacobi forms; weakly holomorphic Jacobi forms
Summary: We derive asymptotic formulas for the coefficients of certain classes of weakly holomorphic Jacobi forms and weakly holomorphic modular forms (not necessarily of integral weight) without using the circle method. Then two applications of these formulas are given. Namely, we estimate the growth of the Fourier coefficients of two important weak Jacobi forms of index \(1\) and non-positive weights and obtain an asymptotic formula for the Fourier coefficients of the modular functions \(\theta ^k/\eta ^l\) for all integers \(k,l\geq 1\), where \(\theta \) is the weight \(1/2\) modular form and \(\eta \) is the Dedekind eta function.