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

2020/01/16 by Soon-Yi Kang, Kang, Soon-Yi
Mathematics · #11F03 #11F12 #11F25 #11F30 #11F33 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2001.05686

openalex publication_date 2020/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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