Jacob's ladders and the nonlocal interaction of the function Z(t) with the function Z²(t) on the distance ∼ (1-c)π(t) for a collection of disconnected sets

2010/06/26 by Jan Moser, Moser, Jan
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1006.5158

arxiv created 2010/07/19 · arxiv updated 2010/07/20

Abstract

It is shown in this paper that there is a fine correlation of the third order between the values of the functions Z[\vp₁(t)] and Z²(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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