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

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

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 Rieman...

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Bibliographic Details
Main Author: Walter Dittrich
Format: Article
Language:English
Published: MDPI AG 2019-03-01
Series:Universe
Subjects:
Riemann
zeta function
functional equation
Heisenberg-Euler Lagrangian
Online Access:http://www.mdpi.com/2218-1997/5/3/79
Description
Summary: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.
ISSN:2218-1997

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