Jacob's ladders and the oscillations of the function $|ζ(1/2+it)|^2$ around its mean-value; law of the almost exact equality of corresponding areas

Details Jacob's ladders and the oscillations of the function $|ζ(1/2+it)|^2$ around its mean-value; law of the almost exact equality of corresponding areas Jacob's ladders and the oscillations of the function $|ζ(1/2+it)|^2$ around its mean-value; law of the almost exact equality of corresponding areas

2010-06-22

arxiv.org/abs/1006.4316v1

Mathematics

Classical Analysis and ODEs

Scientific paper

The oscillations of the function $Z^2(t),\ t\in [0,T]$ around the main part
$\sigma(T)$ of its mean-value are studied in this paper. It is proved that an
almost equality of the corresponding areas holds true. This result cannot be
obtained by methods of Balasubramanian, Heath-Brown and Ivic.

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