Jacob's ladders and vector operator producing new generations of $L_2$-orthogonal systems connected with the Riemann's $ζ(\frac 12+it)$ function

Jan Moser

paper

Jacob's ladders and vector operator producing new generations of $L_{2}$ -orthogonal systems connected with the Riemann's $ζ (\frac{1}{2} + i t)$ function

arXiv:2302.07508

Abstract

In this paper we introduce a generating vector-operator acting on the class of functions $L_{2} ([a, a + 2 l])$ . This operator produces (for arbitrarily fixed $[a, a + 2 l]$ ) infinite number of new generation $L_{2}$ -systems. Every element of the mentioned systems depends on Riemann's zeta-function and on Jacob's ladder.

14 pages, minor typos corrected

Jacob's ladders and vector operator producing new generations of L2​-orthogonal systems connected with the Riemann's ζ(21​+it) function

Abstract

Jacob's ladders and vector operator producing new generations of $L_{2}$ -orthogonal systems connected with the Riemann's $ζ (\frac{1}{2} + i t)$ function