Jacob's ladders and the asymptotic formula for the integral of the eight order expression |ζ(1/2+i\vp₂(t))|⁴|ζ(1/2+it)|⁴

2010/01/13 by Jan Moser, Moser, Jan
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1001.2114

arxiv created 2010/01/19 · arxiv updated 2010/02/26

Abstract

It is proved in this paper that there is a fine correlation between the values of |ζ(1/2+i\vp₂(t))|⁴ and |ζ(1/2+it)|⁴ where \vp₂(t) stands for the Jacob's ladder of the second order. This new asymptotic formula cannot be obtained in known theories of Balasubramanian, Heath-Brown and Ivic.

Related

• Jacob's ladders and the first asymptotic formula for the expression of the sixth order |ζ(1/2+iφ(t)/2)|⁴|ζ(1/2+it)|²
• 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, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations
• Jacob's ladders, the iterations of Jacob's ladder ϕ^k₁(t) and asymptotic formulae for the integrals of the products ... for arbitrary fixed n∈\mbbN
• Jacob's ladders, their iterations and the new class of integrals connected with parts of the Hardy-Littlewood integral of the function |ζ(1/2+it)|²