Asymptotic formulas for the coefficients of certain automorphic functions

• Autorzy: Jaban Meher , Karam Deo Shankhadhar
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11F30: Fourier coefficients of automorphic forms
• 11F50: Jacobi forms
• 11F03: Modular and automorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 169
• Numer: 1
• Strony: 59-76

Daty

wydano

2015

Twórcy

autor

Jaban Meher

• Department of Mathematics, Indian Institute of Science, Bangalore 560012, India

autor

Karam Deo Shankhadhar

• Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Nunoa, Santiago, Chile

Identyfikatory

DOI

10.4064/aa169-1-4