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arXiv · 2403.01787

Effective Weak Universality in Short Intervals

Saeree Wananiyakul·Jörn Steuding·Nithi Rungtanapirom
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Abstract

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 $Ω$-result of Voronin. Furthermore, we also prove the results in short intervals $[T,T+H]$ with $T^ε\le H\le T$ (for any fixed $ε>0$) under the assumption of the Riemann Hypothesis.

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Saeree Wananiyakul, Jörn Steuding, Nithi Rungtanapirom. 2025-01-23. Effective Weak Universality in Short Intervals. https://arxiv.org/abs/2403.01787

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