Divisibility Properties of the Fourier Coefficients of (Mock) Modular Functions and Ramanujan

Abstract

We survey divisibility properties of the Fourier coefficients of modular functions inspired by Ramanujan. Then using recent results of the generalized Hecke operator on harmonic Maass functions and known divisibility of Fourier coefficients of modular functions, we establish congruence relations of the Fourier coefficients of certain modular functions and mock modular functions of various levles.

arXiv comment11 pages