Jacob's ladders and the asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral of the function $|ζ(1/2+it)|^4$

Details Jacob's ladders and the asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral of the function $|ζ(1/2+it)|^4$ Jacob's ladders and the asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral of the function $|ζ(1/2+it)|^4$

2010-01-22

arxiv.org/abs/1001.4007v1

Mathematics

Classical Analysis and ODEs

Scientific paper

The elementary geometric properties of Jacob's ladders of the second order
lead to a class of new asymptotic formulae for short and microscopic parts of
the Hardy-Littlewood integral of $|\zeta(1/2+it)|^4$. These formulae cannot be
obtained by methods of Balasubramanian, Heath-Brown and Ivic.

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