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

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

2009-11-06

arxiv.org/abs/0911.1246v2

Mathematics

Classical Analysis and ODEs

Dedicated to the memory of Anatolij Alekseevich Karatsuba (1937-2008)

Scientific paper

t is proved in this paper that there is a fine correlation between the values
of $|\zeta(1/2+i\varphi(t)/2)|^4$ and $|\zeta(1/2+it)|^2$ which correspond to
two segments with gigantic distance each from other. This new asymptotic
formula cannot be obtained in known theories of Balasubramanian, Heath-Brown
and Ivic.

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