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We demonstrate that the Riemann zeta function zeros define the position andthe widths of the resonances of the quantised Artin dynamical system. The Artindynamical system is defined on the fundamental region of the modular group onthe Lobachevsky plane. It has a finite volume and an infinite extension in thevertical direction that correspond to a cusp. In classical regime the geodesicflow in the fundamental region represents one of the most chaotic dynamicalsystems, has mixing of all orders, Lebesgue spectrum and non-zero Kolmogoroventropy. In quantum-mechanical regime the system can be associated with thenarrow infinitely long waveguide stretched out to infinity along the verticalaxis and a cavity resonator attached to it at the bottom. That suggests aphysical interpretation of the Maass automorphic wave function in the form ofan incoming plane wave of a given energy entering the resonator, bouncinginside the resonator and scattering to infinity. As the energy of the incomingwave comes close to the eigenmodes of the cavity a pronounced resonancebehaviour shows up in the scattering amplitude.

Quantum-Mechanical interpretation of Riemann zeta function zeros