The Role of Riemann's Zeta Function in Mathematics and Physics

被引：3

作者：

Dittrich, Walter ^{[1
]}

机构：

[1] Univ Tubingen, Inst Theoret Phys, Morgenstelle 14, D-72076 Tubingen, Germany

来源：

UNIVERSE | 2019年 / 5卷 / 03期

关键词：

Riemann; zeta function; functional equation; Heisenberg-Euler Lagrangian;

D O I：

10.3390/universe5030079

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

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.

引用

页数：10

共 50 条

[1] Riemann's Zeta Function
Rivat, Joel
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS IN THEIR INTERACTIONS WITH ARITHMETICS AND COMBINATORICS, 2018, 2213 : 27 - 52
[2] On Riemann's function zeta(s).
Bohr, H
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1914, 158 : 1986 - 1988
[3] Hypergeometry and Riemann's zeta function
Krattenthaler, C.
Rivoal, T.
[J]. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 186 (875) : VII - +
[4] On the zeros of Riemann's zeta function
Titchmarsh, EC
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1930, 30 : 319 - 321
[5] Riemann's zeta function and beyond
Gelbart, SS
Miller, SD
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 41 (01) : 59 - 112
[6] Illustrations of Riemann's zeta function
Walther, A
[J]. ACTA MATHEMATICA, 1927, 48 (3-4) : 393 - 400
[7] Inequalities for Riemann's zeta function
Alzer, Horst
[J]. PORTUGALIAE MATHEMATICA, 2009, 66 (03) : 321 - 327
[8] The zeros of the Riemann zeta(s) function
Bohr, H
Landau, E
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1914, 158 : 106 - 110
[9] Polylogarithms and Riemann's zeta function
Lee, MH
[J]. PHYSICAL REVIEW E, 1997, 56 (04): : 3909 - 3912
[10] On the zeros of Riemann's function zeta(s).
Backlund, RJ
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1914, 158 : 1979 - 1981

← 1 2 3 4 5 →