Asymptotic formulas for the coefficients of certain automorphic functions

Jaban Meher, and Karam Deo Shankhadhar. "Asymptotic formulas for the coefficients of certain automorphic functions." Acta Arithmetica 169.1 (2015): 59-76. <http://eudml.org/doc/286536>.

@article{JabanMeher2015,
abstract = {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 $θ^\{k\}/η^\{l\}$ for all integers k,l ≥ 1, where θ is the weight 1/2 modular form and η is the Dedekind eta function.},
author = {Jaban Meher, Karam Deo Shankhadhar},
journal = {Acta Arithmetica},
keywords = {asymptotic formula; Fourier coefficients; weakly holomorphic modular forms; Jacobi-Eisenstein series; weak Jacobi forms; weakly holomorphic Jacobi forms},
language = {eng},
number = {1},
pages = {59-76},
title = {Asymptotic formulas for the coefficients of certain automorphic functions},
url = {http://eudml.org/doc/286536},
volume = {169},
year = {2015},
}

TY - JOUR
AU - Jaban Meher
AU - Karam Deo Shankhadhar
TI - Asymptotic formulas for the coefficients of certain automorphic functions
JO - Acta Arithmetica
PY - 2015
VL - 169
IS - 1
SP - 59
EP - 76
AB - 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 $θ^{k}/η^{l}$ for all integers k,l ≥ 1, where θ is the weight 1/2 modular form and η is the Dedekind eta function.
LA - eng
KW - asymptotic formula; Fourier coefficients; weakly holomorphic modular forms; Jacobi-Eisenstein series; weak Jacobi forms; weakly holomorphic Jacobi forms
UR - http://eudml.org/doc/286536
ER -