The Riemann Zeta Function and Quantum Mechanics

Prof. Dr. Wolfgang P. Schleich, Institut für Quantenphysik und Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, Germany

Abstract:

The Riemann zeta function ζ plays a crucial role in number theory as well as physics. Indeed, the distribution of primes is intimately connected to the non-trivial zeros of this function. We briefly summarize the essential properties of the Riemann zeta function and then present a quantum mechanical system which when measured appropriately yields ζ. We emphasize that for the representation in terms of a Dirichlet series interference [1] suffices to obtain ζ. However, in order to create ζ along the critical line where the non-trivial zeros are located we need two entangled quantum systems [2]. In this way entanglement may be considered the quantum analogue of the analytical continuation of complex analysis. We also analyze the Newton flows [3, 4] of ζ as well as of the closely related function ξ. Both provide additional insight [5] into the Riemann hypothesis.

About DLS:

The Distinguished Lecturer Series (DLS) follows a colloquium format for a broad audience and will be followed by a reception to provide an opportunity for meeting the speaker.