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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/2603.25612 |
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| _version_ | 1866917363177226240 |
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| author | Bruna, Matías |
| author_facet | Bruna, Matías |
| contents | Assuming the generalized Lindelöf hypothesis for Dirichlet $L$-functions, we establish that the least prime $p\equiv a\pmod{q}$ satisfies $p\ll_{\varepsilon} q^{2+\varepsilon}$. This achieves a bound that nearly matches the classical estimate implied by the generalized Riemann hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25612 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A conditional bound for the least prime in an arithmetic progression Bruna, Matías Number Theory Assuming the generalized Lindelöf hypothesis for Dirichlet $L$-functions, we establish that the least prime $p\equiv a\pmod{q}$ satisfies $p\ll_{\varepsilon} q^{2+\varepsilon}$. This achieves a bound that nearly matches the classical estimate implied by the generalized Riemann hypothesis. |
| title | A conditional bound for the least prime in an arithmetic progression |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.25612 |