Jacob's ladders and the asymptotic formula for the integral of the eight order expression $|ζ(1/2+i\vp_2(t))|^4|ζ(1/2+it)|^4$

Details Jacob's ladders and the asymptotic formula for the integral of the eight order expression $|ζ(1/2+i\vp_2(t))|^4|ζ(1/2+it)|^4$ Jacob's ladders and the asymptotic formula for the integral of the eight order expression $|ζ(1/2+i\vp_2(t))|^4|ζ(1/2+it)|^4$

2010-01-13

arxiv.org/abs/1001.2114v2

Mathematics

Classical Analysis and ODEs

Scientific paper

It is proved in this paper that there is a fine correlation between the
values of $|\zeta(1/2+i\vp_2(t))|^4$ and $|\zeta(1/2+it)|^4$ where $\vp_2(t)$
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.

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