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arXiv · 1301.0057

Supremum of the function $S_1(t)$ on short intervals

Takahiro Wakasa
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Abstract

We prove a lower bound on the supremum of the function $S_1(T)$ on short intervals, defined by the integration of the argument of the Riemann zeta-function. The same type of result on the supremum of $S(T)$ have already been obtained by Karatsuba and Korolev. Our result is based on the idea of the paper of Karatsuba and Korolev. Also, we show an improved Omega-result for a lower bound.

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Takahiro Wakasa. 2013-11-18. Supremum of the function $S_1(t)$ on short intervals. https://arxiv.org/abs/1301.0057

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