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

2010/07/29 by Jan Moser, Moser, Jan
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematics and Applications #math.CA

paper · pdf · doi:10.48550/arxiv.1007.5147

arxiv created 2010/07/29 · openalex publication_date 2010/07/29 · arxiv updated 2010/07/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

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