Effective Weak Universality in Short Intervals

We prove an effective universality theorem of the Riemann zeta-function in short intervals \([T,T+H]\) with \(T^{\frac{27}{82}}\le H\le T\) by following an effective multidimensional \(\Omega\)-result of Voronin. Furthermore, we also prove the results in short intervals \([T,T+H]\) with \(T^\epsilon...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Wananiyakul, Saeree, Steuding, Jörn, Rungtanapirom, Nithi
Format: Article
Language:English
Subjects:
Intervals
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Summary:We prove an effective universality theorem of the Riemann zeta-function in short intervals \([T,T+H]\) with \(T^{\frac{27}{82}}\le H\le T\) by following an effective multidimensional \(\Omega\)-result of Voronin. Furthermore, we also prove the results in short intervals \([T,T+H]\) with \(T^\epsilon\le H\le T\) (for any fixed \(\epsilon>0\)) under the assumption of the Riemann Hypothesis.
ISSN:2331-8422