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arXiv · 1001.1632

Jacob's ladders, the iterations of Jacob's ladder $ϕ^k_1(t)$ and asymptotic formulae for the integrals of the products ... for arbitrary fixed $n\in\mbb{N}$

Jan Mozer
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Abstract

In this paper we introduce the iterations $ϕ^k_1(t)$ of the Jacob's ladder. It is proved, for example, that the mean-value of the product $$Z^2[ϕ^n_1(t)]Z^2[ϕ^{n-1}(t)]... Z^2[ϕ^0_1(t)]$$ over the segment $[T,T+U]$ is asymptotically equal to $\ln^{n+1}T$. Nor the case $n=1$ cannot be obtained in known theories of Balasubramanian, Heath-Brown and Ivic.

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Jan Mozer. 2010-01-11. Jacob's ladders, the iterations of Jacob's ladder $ϕ^k_1(t)$ and asymptotic formulae for the integrals of the products ... for arbitrary fixed $n\in\mbb{N}$. https://arxiv.org/abs/1001.1632

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