Discrete $Ω$-results for the Riemann zeta function
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910553475121152 |
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| author | Minelli, Paolo Sourmelidis, Athanasios |
| author_facet | Minelli, Paolo Sourmelidis, Athanasios |
| contents | We study lower bounds for the Riemann zeta function $ζ(s)$ along vertical arithmetic progressions in the right-half of the critical strip. We show that the lower bounds obtained in the discrete case coincide, up to the constants in the exponential, with the ones known for the continuous case, that is when the imaginary part of $s$ ranges on a given interval. Our methods are based on a discretization of the resonance method for estimating extremal values of $ζ(s)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08011 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Discrete $Ω$-results for the Riemann zeta function Minelli, Paolo Sourmelidis, Athanasios Number Theory 11M06 We study lower bounds for the Riemann zeta function $ζ(s)$ along vertical arithmetic progressions in the right-half of the critical strip. We show that the lower bounds obtained in the discrete case coincide, up to the constants in the exponential, with the ones known for the continuous case, that is when the imaginary part of $s$ ranges on a given interval. Our methods are based on a discretization of the resonance method for estimating extremal values of $ζ(s)$. |
| title | Discrete $Ω$-results for the Riemann zeta function |
| topic | Number Theory 11M06 |
| url | https://arxiv.org/abs/2312.08011 |