Jacob's ladders and the asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral of the function |ζ(1/2+it)|⁴

2010/01/22 by Jan Moser, Moser, Jan
Mathematics · #Algebraic and Geometric Analysis #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #advanced mathematical theories #math.CA

paper · pdf · doi:10.48550/arxiv.1001.4007

arxiv created 2010/01/22 · openalex publication_date 2010/01/22 · arxiv updated 2010/02/26 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The elementary geometric properties of Jacob's ladders of the second order lead to a class of new asymptotic formulae for short and microscopic parts of the Hardy-Littlewood integral of |ζ(1/2+it)|⁴. These formulae cannot be obtained by methods of Balasubramanian, Heath-Brown and Ivic.

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