Jacob's ladders and some new consequences from A. Selberg's formula

Details Jacob's ladders and some new consequences from A. Selberg's formula Jacob's ladders and some new consequences from A. Selberg's formula

2010-10-05

arxiv.org/abs/1010.0868v1

Mathematics

Classical Analysis and ODEs

Scientific paper

It is proved in this paper that the Jacob's ladders together with the A.
Selberg's classical formula (1942) lead to a new kind of formulae for some
short trigonometric sums. These formulae cannot be obtained in the classical
theory of A. Selberg, and all the less, in the theories of Balasubramanian,
Heath-Brown and Ivic.

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