Low-lying zeros of a large orthogonal family of automorphic $L$-functions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910584851660800 |
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| author | Baluyot, Siegfred Chandee, Vorrapan Li, Xiannan |
| author_facet | Baluyot, Siegfred Chandee, Vorrapan Li, Xiannan |
| contents | We study a new orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q \asymp Q$. To illustrate our methods, we prove a one level density result for this family with the support of the Fourier transform of the test function being extended to be inside $(-4, 4)$. The main techniques developed in this paper will be useful in developing further results for this family, including estimates for high moments, information on the vertical distribution of zeros, as well as critical line theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07606 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Low-lying zeros of a large orthogonal family of automorphic $L$-functions Baluyot, Siegfred Chandee, Vorrapan Li, Xiannan Number Theory We study a new orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q \asymp Q$. To illustrate our methods, we prove a one level density result for this family with the support of the Fourier transform of the test function being extended to be inside $(-4, 4)$. The main techniques developed in this paper will be useful in developing further results for this family, including estimates for high moments, information on the vertical distribution of zeros, as well as critical line theorems. |
| title | Low-lying zeros of a large orthogonal family of automorphic $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2310.07606 |