Jacob's ladders and some new consequences from A. Selberg's formula
Jan Moser
TL;DR
This paper introduces new formulas for short trigonometric sums derived from Jacob's ladders and Selberg's classical formula, which are not accessible through traditional methods in analytic number theory.
Contribution
It presents novel formulas for short trigonometric sums using Jacob's ladders and Selberg's formula, expanding the analytical tools beyond classical approaches.
Findings
New formulas for short trigonometric sums derived from Jacob's ladders and Selberg's formula
These formulas are not obtainable via classical Selberg theory or related methods
Enhanced understanding of trigonometric sums in analytic number theory
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.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Mathematics and Applications