# Jacob&#x27;s ladders and the nonlocal interaction of the function $Zt$ with the function $ilde{Z}^2t$ on the distance $sim 1-cπt$ for a collection of disconnected sets - Mathematics > Classical Analysis and ODEs

Jacob&#x27;s ladders and the nonlocal interaction of the function $Zt$ with the function $ilde{Z}^2t$ on the distance $sim 1-cπt$ for a collection of disconnected sets - Mathematics > Classical Analysis and ODEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: It is shown in this paper that there is a fine correlation of the third orderbetween the values of the functions $Z\vp 1t$ and $\tilde{Z}^2t$ whichcorresponds to two collections of disconnected sets. The corresponding newasymptotic formula cannot be obtained within known theories of Balasubramanian,Heath-Brown and Ivic.

Author: Jan Moser

Source: https://arxiv.org/