On values of weakly holomorphic modular functions at divisors of meromorphic modular forms

2021/07/02 by Daeyeol Jeon, Soon-Yi Kang, Jeon, Daeyeol +3
Mathematics · #11F03 #11F12 #11F25 #11J81 #11J91 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2107.01158

openalex publication_date 2021/07/02 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We show that the values of a certain family of weakly holomorphic modular functions at points in the divisors of any meromorphic modular form with algebraic Fourier coefficients are algebraic. We use this to extend the classical result of Schneider by proving that zeros or poles of any non-zero meromorphic modular form with algebraic Fourier coefficients are either transcendental or imaginary quadratic irrational.

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