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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.01711 |
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| _version_ | 1866915827865878528 |
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| author | Arguin, Louis-Pierre Creighton, Nathan |
| author_facet | Arguin, Louis-Pierre Creighton, Nathan |
| contents | Building on work in \cite{AB24} on the Riemann zeta function at height $T$ off the critical line, we prove an unconditional lower bound on the critical line for real large deviations of the order $V\simα\log\log T$ for any $α>0.$ This gives another proof of the sharpest known unconditional lower bounds on the fractional moments of the Riemann zeta function, due to \cite{HSlower}. The lower bound on large deviations is of the same order of magnitude as the upper bound proved in \cite{AB23}, for the range $0<α<2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01711 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lower bounds for the large deviations and moments of the Riemann zeta function on the critical line Arguin, Louis-Pierre Creighton, Nathan Number Theory 11M06, 11M50, 60F10, 60G50 Building on work in \cite{AB24} on the Riemann zeta function at height $T$ off the critical line, we prove an unconditional lower bound on the critical line for real large deviations of the order $V\simα\log\log T$ for any $α>0.$ This gives another proof of the sharpest known unconditional lower bounds on the fractional moments of the Riemann zeta function, due to \cite{HSlower}. The lower bound on large deviations is of the same order of magnitude as the upper bound proved in \cite{AB23}, for the range $0<α<2.$ |
| title | Lower bounds for the large deviations and moments of the Riemann zeta function on the critical line |
| topic | Number Theory 11M06, 11M50, 60F10, 60G50 |
| url | https://arxiv.org/abs/2603.01711 |