A central limit theorem for coefficients of $L$-functions in short intervals
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909427753287680 |
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| author | Leung, Sun-Kai |
| author_facet | Leung, Sun-Kai |
| contents | Assuming the generalized Lindelöf hypothesis (GLH), a weak version of the generalized Ramanujan conjecture and a Rankin--Selberg type partial sum estimate, we establish the normality of the sum of coefficients of a general $L$-function in short intervals of appropriate length. The novelty lies in the degree aspect under GLH. In particular, this generalizes the result of Hughes and Rudnick on lattice point counts in thin annuli. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A central limit theorem for coefficients of $L$-functions in short intervals Leung, Sun-Kai Number Theory Probability 11F30, 60F05 Assuming the generalized Lindelöf hypothesis (GLH), a weak version of the generalized Ramanujan conjecture and a Rankin--Selberg type partial sum estimate, we establish the normality of the sum of coefficients of a general $L$-function in short intervals of appropriate length. The novelty lies in the degree aspect under GLH. In particular, this generalizes the result of Hughes and Rudnick on lattice point counts in thin annuli. |
| title | A central limit theorem for coefficients of $L$-functions in short intervals |
| topic | Number Theory Probability 11F30, 60F05 |
| url | https://arxiv.org/abs/2405.14834 |