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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.22124 |
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| _version_ | 1866917358170275840 |
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| author | Earnst, Adam |
| author_facet | Earnst, Adam |
| contents | We prove asymptotics for mollified first and second moments of subfamilies of Dirichlet $L$-functions given by shrinking angular restrictions on the root number. Using these moments, we prove that for even primitive characters with prime conductor $q$, a positive proportion of the central values $L(1/2,χ)$ do not vanish as $q\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22124 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Vanishing of Dirichlet $L$-functions at the central point with restricted root number Earnst, Adam Number Theory 11M20 (Primary) 11L05, 11T23 (Secondary) We prove asymptotics for mollified first and second moments of subfamilies of Dirichlet $L$-functions given by shrinking angular restrictions on the root number. Using these moments, we prove that for even primitive characters with prime conductor $q$, a positive proportion of the central values $L(1/2,χ)$ do not vanish as $q\to\infty$. |
| title | Non-Vanishing of Dirichlet $L$-functions at the central point with restricted root number |
| topic | Number Theory 11M20 (Primary) 11L05, 11T23 (Secondary) |
| url | https://arxiv.org/abs/2603.22124 |