Jacob's ladders and the multiplicative asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral

2009/07/02 by Jan Moser, Moser, Jan
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.0907.0301

5 pages

arxiv created 2009/07/02 · arxiv updated 2009/12/01

Abstract

The elementary geometric properties of Jacob's ladders lead to a class of new asymptotic formulae for short and microscopic parts of the Hardy-Littlewood integral. This class of asymptotic formulae cannot be obtained by methods of Balasubramanian, Heath-Brown and Ivic.

Related

• 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
• Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integral
• Jacob's ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations
• Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918) and their relation to the Titchmarsh's sums (1943) and the Fermat-Wiles theorem
• Jacob's ladders, existence of almost linear increments of the Hardy-Littlewood integral and new types of multiplicative laws