Jacob's ladders and the first asymptotic formula for the expression of the fifth order Z³[...]Z²(t) for the collection of disconnected sets

2009/12/01 by Jan Moser, Moser, Jan · 3 citations
Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #math.CA

paper · pdf · doi:10.48550/arxiv.0912.0130

arxiv created 2009/12/01 · openalex publication_date 2009/12/01 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown in this paper that there is a fine correlation of the fifth order between the values Z[ϕ(t)/2+ρ₁]Z[ϕ(t)/2+ρ₂]Z[ϕ(t)/2+ρ₃] and Z²(t) which correspond to two collections of disconnected sets. This new asymptotic formula cannot be obtained within known theories of Balasubramanian, Heath-Brown and Ivic.

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