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The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡

Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany
This article is dedicated to Martin Reuter on the occasion of his 60th birthday, as well as to a mutual hero of ours: Bernhard Riemann.
This paper is based on a talk given at the conference “Quantum Fields—From Fundamental Concepts to Phenomenological Questions”, Mainz, Germany, 26–28 September 2018.
Universe 2019, 5(3), 79; https://doi.org/10.3390/universe5030079
Received: 28 January 2019 / Revised: 28 February 2019 / Accepted: 11 March 2019 / Published: 14 March 2019
In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Riemann’s zeta function to regularize the otherwise infinite results of the so-called Heisenberg–Euler Lagrangian. As a spin-off, we also calculate some integrals that are useful in mathematics and physics. View Full-Text
Keywords: Riemann; zeta function; functional equation; Heisenberg-Euler Lagrangian Riemann; zeta function; functional equation; Heisenberg-Euler Lagrangian
MDPI and ACS Style

Dittrich, W. The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡. Universe 2019, 5, 79.

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