Jacob's ladders and the nonlocal interaction of the function $Z(t)$ with the function $\tilde{Z}^2(t)$ on the distance $\sim (1-c)π(t)$ for a collection of disconnected sets

Details Jacob's ladders and the nonlocal interaction of the function $Z(t)$ with the function $\tilde{Z}^2(t)$ on the distance $\sim (1-c)π(t)$ for a collection of disconnected sets Jacob's ladders and the nonlocal interaction of the function $Z(t)$ with the function $\tilde{Z}^2(t)$ on the distance $\sim (1-c)π(t)$ for a collection of disconnected sets

2010-06-26

arxiv.org/abs/1006.5158v2

Mathematics

Classical Analysis and ODEs

Scientific paper

It is shown in this paper that there is a fine correlation of the third order
between the values of the functions $Z[\vp_1(t)]$ and $\tilde{Z}^2(t)$ which
corresponds to two collections of disconnected sets. The corresponding new
asymptotic formula cannot be obtained within known theories of Balasubramanian,
Heath-Brown and Ivic.

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