Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914161942855680 |
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| author | Ross, Erick |
| author_facet | Ross, Erick |
| contents | Fix a prime $p$, and let $\widehat T_p^{\mathrm{new}}(N,k,χ) := χ(p)^{-1/2} p^{-(k-1)/2} T_p^{\mathrm{new}}(N,k,χ)$ denote the normalized $p$'th Hecke operator over the newspace with nenbentypus $S_k^{\mathrm{new}}(N,χ)$. In this paper, we determine the distribution of the eigenvalues of $\widehat T_p^{\mathrm{new}}(N,k,χ)$ as $N+k \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus Ross, Erick Number Theory Primary: 11F11, Secondary: 11F25, 11F72 Fix a prime $p$, and let $\widehat T_p^{\mathrm{new}}(N,k,χ) := χ(p)^{-1/2} p^{-(k-1)/2} T_p^{\mathrm{new}}(N,k,χ)$ denote the normalized $p$'th Hecke operator over the newspace with nenbentypus $S_k^{\mathrm{new}}(N,χ)$. In this paper, we determine the distribution of the eigenvalues of $\widehat T_p^{\mathrm{new}}(N,k,χ)$ as $N+k \to \infty$. |
| title | Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus |
| topic | Number Theory Primary: 11F11, Secondary: 11F25, 11F72 |
| url | https://arxiv.org/abs/2511.13966 |