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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.14796 |
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| _version_ | 1866913871380348928 |
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| author | Zhu, Xiao-Jie |
| author_facet | Zhu, Xiao-Jie |
| contents | We give explicit formulae for a class of complex linear unitary characters of the congruence subgroups $Γ_0(N)$ which involve a variant of Rademacher's $Ψ$ function. We then prove that these characters cover all characters of $Γ_0(N)$ precisely when $N=1,2,3,4,5,6,7,8,10,12,13$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14796 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit formulae for linear characters of $Γ_0(N)$ Zhu, Xiao-Jie Number Theory Primary 11F06, Secondary 11F20, 22D10, 20F05, 20H10 We give explicit formulae for a class of complex linear unitary characters of the congruence subgroups $Γ_0(N)$ which involve a variant of Rademacher's $Ψ$ function. We then prove that these characters cover all characters of $Γ_0(N)$ precisely when $N=1,2,3,4,5,6,7,8,10,12,13$. |
| title | Explicit formulae for linear characters of $Γ_0(N)$ |
| topic | Number Theory Primary 11F06, Secondary 11F20, 22D10, 20F05, 20H10 |
| url | https://arxiv.org/abs/2402.14796 |