Jacob's ladders and the nonlocal interaction of the function |ζ(1/2+it)| with the function argζ(1/2+it) on the distance ∼(1-c)π(t)

2010/04/01 by Jan Moser, Moser, Jan
Mathematics · #Mathematical and Theoretical Analysis #Mathematics and Applications #advanced mathematical theories #math.CA

paper · pdf · doi:10.48550/arxiv.1004.0169

arxiv created 2010/06/18 · arxiv updated 2010/06/21

Abstract

In this paper we obtain a new-type formula - a mixed formula - which connects the functions |ζ(1/2+it)| and argζ(1/2+it). This formula cannot be obtained in the classical theory of A. Selberg, and, all the less, in the theories of Balasubramanian, Heath-Brown and Ivic.

Related

• Jacob's ladders and the nonlocal interaction of the function Z(t) with the function Z²(t) on the distance ∼ (1-c)π(t) for a collection of disconnected sets
• Jacob's ladders and the nonlocal interaction of the function Z²(t) with the function Z²(t) on the distance ∼ (1-c)π(t) for the collections of disconnected sets
• Jacob's ladders and the first asymptotic formula for the expression of the sixth order |ζ(1/2+iφ(t)/2)|⁴|ζ(1/2+it)|²
• Jacob's ladders, new properties of the function arg\zf and corresponding metamorphoses
• Jacob's ladders, interactions between ζ-oscillating systems and ζ-analogue of an elementary trigonometric identity