An Analogue of the Dedekind Eta Function for Hecke Groups $H(\sqrt{D})$

Fuente: arXiv
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Main Authors: Basak, Debmalya, Goldfeld, Dorian, Heap, Winston, Robles, Nicolas, Zaharescu, Alexandru
Format: Preprint
Published: 2025
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author Basak, Debmalya
Goldfeld, Dorian
Heap, Winston
Robles, Nicolas
Zaharescu, Alexandru
author_facet Basak, Debmalya
Goldfeld, Dorian
Heap, Winston
Robles, Nicolas
Zaharescu, Alexandru
contents Let $D\equiv 1\bmod{4}$ be a fundamental discriminant of a real quadratic field. We construct an analogue of the classical Dedekind eta function for the Hecke group $H(\sqrt{D})$. This gives rise to a new family of holomorphic modular functions for $H(\sqrt{D})$ which vanish at the cusp at $\infty$. We establish results on the asymptotic growth and sign patterns of the Fourier coefficients associated to these modular forms.
format Preprint
id arxiv_https___arxiv_org_abs_2508_21239
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An Analogue of the Dedekind Eta Function for Hecke Groups $H(\sqrt{D})$
Basak, Debmalya
Goldfeld, Dorian
Heap, Winston
Robles, Nicolas
Zaharescu, Alexandru
Number Theory
Let $D\equiv 1\bmod{4}$ be a fundamental discriminant of a real quadratic field. We construct an analogue of the classical Dedekind eta function for the Hecke group $H(\sqrt{D})$. This gives rise to a new family of holomorphic modular functions for $H(\sqrt{D})$ which vanish at the cusp at $\infty$. We establish results on the asymptotic growth and sign patterns of the Fourier coefficients associated to these modular forms.
title An Analogue of the Dedekind Eta Function for Hecke Groups $H(\sqrt{D})$
topic Number Theory
url https://arxiv.org/abs/2508.21239