On the zeros of weakly holomorphic modular forms

TL;DR

This paper investigates the zeros of weakly holomorphic modular forms, focusing on their transcendental nature at higher levels and Fricke groups, and explores the algebraic independence of their values.

Contribution

It extends previous work by analyzing transcendental zeros for modular forms of higher levels and certain Fricke groups, and studies algebraic independence of their values.

Findings

Transcendental zeros identified for higher level modular forms.

Results extend Kohnen's work on zeros of modular forms.

Algebraic independence of modular form values demonstrated.

Abstract

In this article, we study the nature of zeros of weakly holomorphic modular forms. In particular, we prove results about transcendental zeros of modular forms of higher levels and for certain Fricke groups which extend a work of Kohnen. Furthermore, we investigate the algebraic independence of values of weakly holomorphic modular forms.