The $n^{th}$ centered moments of a large orthogonal family of automorphic $L$-functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918185811312640 |
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| author | Chandee, Vorrapan Lee, Yoonbok Li, Xiannan |
| author_facet | Chandee, Vorrapan Lee, Yoonbok Li, Xiannan |
| contents | We obtain the $n$th centered moments of one level densities of a large orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q\sim Q$. We verify the Katz-Sarnak conjecture for these statistics, in the range where the sum of the supports of the Fourier transforms of test functions lies in $(-4, 4)$. In so doing, we need to understand certain phantom oversized terms, which allow us to extract the right off-diagonal contributions. We further need to resolve the combinatorial problem that arises when matching our main terms with random matrix predictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $n^{th}$ centered moments of a large orthogonal family of automorphic $L$-functions Chandee, Vorrapan Lee, Yoonbok Li, Xiannan Number Theory 11M50, 11F11, 11F72 We obtain the $n$th centered moments of one level densities of a large orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q\sim Q$. We verify the Katz-Sarnak conjecture for these statistics, in the range where the sum of the supports of the Fourier transforms of test functions lies in $(-4, 4)$. In so doing, we need to understand certain phantom oversized terms, which allow us to extract the right off-diagonal contributions. We further need to resolve the combinatorial problem that arises when matching our main terms with random matrix predictions. |
| title | The $n^{th}$ centered moments of a large orthogonal family of automorphic $L$-functions |
| topic | Number Theory 11M50, 11F11, 11F72 |
| url | https://arxiv.org/abs/2510.07647 |