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

Abstract

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.

References in corpus (6)

• Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integral
• Jacob's ladders and the multiplicative asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral
• Jacob's ladders and the quantization of the Hardy-Littlewood integral
• Jacob's ladders and the first asymptotic formula for the expression of the fifth order $Z^3[...]{\hat{Z}}^2(t)$ for the collection of disconnected sets
• Jacob's ladders and the almost exact asymptotic representation of the Hardy-Littlewood integral
• Jacob's ladders and the asymptotically approximate solutions of a nonlinear diophantine equation