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arXiv · 0912.0130

Jacob's ladders and the first asymptotic formula for the expression of the fifth order $Z^3[...]\hat{Z}^2(t)$ for the collection of disconnected sets

Jan Moser
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Abstract

It is shown in this paper that there is a fine correlation of the fifth order between the values $Z[ϕ(t)/2+ρ_1]Z[ϕ(t)/2+ρ_2]Z[ϕ(t)/2+ρ_3]$ and $\hat{Z}^2(t)$ which correspond to two collections of disconnected sets. This new asymptotic formula cannot be obtained within known theories of Balasubramanian, Heath-Brown and Ivic.

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Jan Moser. 2009-12-01. Jacob's ladders and the first asymptotic formula for the expression of the fifth order $Z^3[...]\hat{Z}^2(t)$ for the collection of disconnected sets. https://arxiv.org/abs/0912.0130

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