On Dirichlet eigenvalues of regular polygons

Berghaus, David; Georgiev, Bogdan; Monien, Hartmut; Radchenko, Danylo

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.jmaa.2024.128460

Permalink :

http://hdl.handle.net/20.500.12210/118885

Title :

On Dirichlet eigenvalues of regular polygons

Author(s) :

Berghaus, David [Auteur]
Fraunhofer Institute for Intelligent Analysis and Information Systems [Fraunhofer IAIS]
Georgiev, Bogdan [Auteur]
Fraunhofer Institute for Intelligent Analysis and Information Systems [Fraunhofer IAIS]
Monien, Hartmut [Auteur]
Bethe Center for Theoretical Physics [BCTP]
Radchenko, Danylo [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Mathematical Analysis and Applications

Pages :

128460

Publisher :

Elsevier

Publication date :

2024-04-25

ISSN :

0022-247X

English keyword(s) :

Dirichlet eigenvalues
Regular polygons
Multiple zeta values
Asymptotics

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We prove that the first Dirichlet eigenvalue of a regular $N$-gon of area $\pi$ has an asymptotic expansion of the form $\lambda_1*(1+\sum_{n\ge3}C_n(\lambda_1)N^{-n})$ where $\lambda_1$ is the first Dirichlet eigenvalue ...
Show more >We prove that the first Dirichlet eigenvalue of a regular $N$-gon of area $\pi$ has an asymptotic expansion of the form $\lambda_1*(1+\sum_{n\ge3}C_n(\lambda_1)N^{-n})$ where $\lambda_1$ is the first Dirichlet eigenvalue of the unit disk and $C_n$ 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 $n \le 14$.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2024-11-22T04:34:18Z

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