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arXiv · 1001.2114

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

Jan Moser
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Abstract

It is proved in this paper that there is a fine correlation between the values of $|ζ(1/2+i\vp_2(t))|^4$ and $|ζ(1/2+it)|^4$ 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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Jan Moser. 2010-01-19. Jacob's ladders and the asymptotic formula for the integral of the eight order expression $|ζ(1/2+i\vp_2(t))|^4|ζ(1/2+it)|^4$. https://arxiv.org/abs/1001.2114

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