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arXiv · 2508.21239

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

Debmalya Basak·Dorian Goldfeld·Winston Heap·Nicolas Robles·Alexandru Zaharescu
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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.

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Debmalya Basak, Dorian Goldfeld, Winston Heap, Nicolas Robles, Alexandru Zaharescu. 2025-08-28. An Analogue of the Dedekind Eta Function for Hecke Groups $H(\sqrt{D})$. https://arxiv.org/abs/2508.21239

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