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

Debmalya Basak; Dorian Goldfeld; Winston Heap; Nicolas Robles; Alexandru Zaharescu

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

Number Theory 2026-03-17 v3

Authors: Debmalya Basak , Dorian Goldfeld , Winston Heap , Nicolas Robles , Alexandru Zaharescu

Abstract

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.

Keywords

Dedekind eta function Hecke group modular forms Fourier coefficients holomorphic modular functions

Cite

@article{arxiv.2508.21239,
  title  = {An Analogue of the Dedekind Eta Function for Hecke Groups $H(\sqrt{D})$},
  author = {Debmalya Basak and Dorian Goldfeld and Winston Heap and Nicolas Robles and Alexandru Zaharescu},
  journal= {arXiv preprint arXiv:2508.21239},
  year   = {2026}
}

Comments

Significant changes. New results added and Winston Heap is now a co-author

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

Abstract

Keywords

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