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Publication

KIAM Preprint № 5, Moscow, 2004
Authors: Pustyl'nikov L. D.
On the representation of Riemann zeta-function in the critical strip over an infinite product of second-order matrics and on a dynamical system
Abstract:
The representations of Riemann zeta-function over an infinite products of second-order matrics converging in the critical strip are obtained. This result allows to construct a dynamical system is connected with Riemann problem on zeros of the zeta-function so that a second-order periodic trajectory of a special type corresponds to every complex zero not situated on the critical line. A certain operator acting in a Hilbert space, which has an eigenvector with eigenvalue (-1) if an only if Riemann zeta-function has a complex zero not situated on the critical line, is used in the construction of a dynamical system.
Publication language: russian, pages: 11
Research direction:
Mathematical problems and theory of numerical methods
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