Trace Formulas Applied to the Riemann ζ-Function

DOI10.1007/978-3-030-20087-9_8zbMath1440.11086arXiv1812.00459OpenAlexW2903156072MaRDI QIDQ4973360

Klaus Kirsten, Mark S. Ashbaugh, Lotfi Hermi, Lance L. Littlejohn, Friedrich Gesztesy, Hagop Tossounian

Publication date: 3 December 2019

Published in: Integrability, Supersymmetry and Coherent States (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.00459

zbMATH Keywords

Riemann zeta functionspectral theoryDirichlet Laplaciantrace formulastrace class operators

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integral and series representations of Riemann's zeta function and Dirichlet's eta function and a medley of related results
• Ten physical applications of spectral zeta functions.
• An elementary proof of the irrationality of Tschakaloff series
• Zeta function regularization of path integrals in curved spacetime
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• Euclidean quantum gravity on manifolds with boundary
• Functional determinants by contour integration methods.
• Effective computation of traces, determinants, and \(\zeta\)-functions for Sturm-Liouville operators
• The functional calculus for sectorial operators
• R-torsion and the Laplacian on Riemannian manifolds
• Trace formulas for Sturm-Liouville differential operators
• A Note on the Irrationality of ζ(2) and ζ(3)
• Functional determinants for general Sturm–Liouville problems
• Advances in the Casimir Effect

This page was built for publication: Trace Formulas Applied to the Riemann ζ-Function