On Dirichlet eigenvalues of regular polygons

We prove that the first Dirichlet eigenvalue of a regular N-gon of area π has an asymptotic expansion of the form λ1(1+∑n≥3Cn(λ1)Nn) as N→∞, where λ1 is the first Dirichlet eigenvalue of the unit disk and Cn are polynomials whose coefficients belong to the space of multiple zeta values of weight n a...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 538; no. 2; p. 128460
Main Authors Berghaus, David, Georgiev, Bogdan, Monien, Hartmut, Radchenko, Danylo
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.10.2024
Subjects
Asymptotics
Dirichlet eigenvalues
Multiple zeta values
Regular polygons
Multiple zeta values
Dirichlet eigenvalues
Asymptotics
Regular polygons
Online AccessGet full text

Cover

More Information
Summary:We prove that the first Dirichlet eigenvalue of a regular N-gon of area π has an asymptotic expansion of the form λ1(1+∑n≥3Cn(λ1)Nn) as N→∞, where λ1 is the first Dirichlet eigenvalue of the unit disk and Cn are polynomials whose coefficients belong to the space of multiple zeta values of weight n and conjecture that their coefficients lie in the space of single-valued multiple zeta values. We also explicitly compute these polynomials for all n≤14.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128460