An Analogue of the Dedekind Eta Function for Hecke Groups $H(\sqrt{D})$
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915866269974528 |
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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 |