Zeros of $L$-functions in families near the critical line
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913559689035776 |
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| author | Blomer, Valentin Thorner, Jesse |
| author_facet | Blomer, Valentin Thorner, Jesse |
| contents | We combine the relative trace formula with analytic methods to obtain zero density estimate for $L$-functions in various families of automorphic representations for $\mathrm{GL}(m)$. Applications include strong bounds for the average analytic rank of these $L$-functions at the central point and average equidistribution results for the imaginary parts of the zeros. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zeros of $L$-functions in families near the critical line Blomer, Valentin Thorner, Jesse Number Theory 11M41, 11M26, 11F70 We combine the relative trace formula with analytic methods to obtain zero density estimate for $L$-functions in various families of automorphic representations for $\mathrm{GL}(m)$. Applications include strong bounds for the average analytic rank of these $L$-functions at the central point and average equidistribution results for the imaginary parts of the zeros. |
| title | Zeros of $L$-functions in families near the critical line |
| topic | Number Theory 11M41, 11M26, 11F70 |
| url | https://arxiv.org/abs/2410.17158 |