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

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

2011-03-02

arxiv.org/abs/1103.0359v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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