Jacob's ladders and the asymptotically approximate solutions of a nonlinear diophantine equation

2010/01/18 by Jan Moser, Moser, Jan
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Benford’s Law and Fraud Detection #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CA

paper · pdf · doi:10.48550/arxiv.1001.3019

arxiv created 2010/01/18 · openalex publication_date 2010/01/18 · arxiv updated 2010/02/26 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

The nonlinear equation which is connected with the main term of the Hardy-Littlewood formula for ζ²(1/2+it) is studied. In this direction I obtain the fine results which cannot be reached by published methods of Balasubramanian, Heath-Brown and Ivic in the field of the Hardy-Littlewood integral.

Citations

• Jacob's ladders and the first asymptotic formula for the expression of the fifth order Z³[...]Z²(t) for the collection of disconnected sets
• Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integral

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