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arXiv · 1004.0169

Jacob's ladders and the nonlocal interaction of the function $|\zeta(1/2+it)|$ with the function $\arg\zeta(1/2+it)$ on the distance $\sim(1-c)\pi(t)$

Jan Moser
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Abstract

In this paper we obtain a new-type formula - \emph{a mixed formula} - which connects the functions $|\zeta(1/2+it)|$ and $\arg\zeta(1/2+it)$. This formula cannot be obtained in the classical theory of A. Selberg, and, all the less, in the theories of Balasubramanian, Heath-Brown and Ivic.

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Jan Moser. 2010-04-01. Jacob's ladders and the nonlocal interaction of the function $|\zeta(1/2+it)|$ with the function $\arg\zeta(1/2+it)$ on the distance $\sim(1-c)\pi(t)$. https://arxiv.org/abs/1004.0169

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