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

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

2010-07-29

arxiv.org/abs/1007.5147v1

Mathematics

Classical Analysis and ODEs

Scientific paper

It is shown in this paper that there is a fine correlation of the fourth
order between the functions $Z^2[\vp_1(t)]$ and $\tilde{Z}^2(t)$, respectively.
This correlation is with respect to two collections of disconnected sets.
Corresponding new asymptotic formulae cannot be obtained within known theories
of Balasubramanian, Heath-Brown and Ivic.

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