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arXiv · 1103.0359

Jacob's ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations

Jan Moser
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Abstract

In this paper we obtain new formulae for short and microscopic parts of the Hardy-Littlewood integral, and the first asymptotic formula for the sixth order expression $|\zeta(\frac{1}{2}+i\vp_1(t))|^4|\zf|^2$. These formulae cannot be obtained in the theories of Balasubramanian, Heath-Brown and Ivic. Dedicated to the 75th aniversary of Anatolii Alekseevich Karatsuba.

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Jan Moser. 2011-03-02. Jacob's ladders, the structure of the Hardy-Littlewood integral and some new class of nonlinear integral equations. https://arxiv.org/abs/1103.0359

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