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

Jan Moser

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arXiv · 1006.4316

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

Jan Moser

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Abstract

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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Jan Moser. 2010-06-22. Jacob's ladders and the oscillations of the function $|\zeta(1/2+it)|^2$ around its mean-value; law of the almost exact equality of corresponding areas. https://arxiv.org/abs/1006.4316

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