On the zeros of certain modular functions for the normalizers of congruence subgroups of low levels II

TL;DR

This paper investigates the zeros of Eisenstein series and related modular functions for genus zero normalizers of low-level congruence subgroups, using numerical methods to analyze their distribution.

Contribution

It provides a numerical analysis of the zeros of these modular functions for specific low-level congruence subgroups, extending previous theoretical work.

Findings

Zeros are distributed in specific patterns around the fundamental domain.

Numerical results support conjectures about zero locations for these functions.

The study enhances understanding of modular function zeros for low-level groups.

Abstract

We research the location of the zeros of the Eisenstein series and the modular functions from the Hecke type Faber polynomials associated with the normalizers of congruence subgroups which are of genus zero and of level at most twelve. In Part II, we will observe the location of the zeros of the above functions by numerical calculation.