On Dirichlet eigenvalues of regular polygons
type: Item
instance of: scholarly article
title: On Dirichlet eigenvalues of regular polygons
author: Q6203469
author: Bogdan Georgiev
author: Hartmut Monien
author: Danylo V. Radchenko
published in: Journal of Mathematical Analysis and Applications
publication date: 2024-06-19T00:00:00Z
review text: Let \(\mathcal{P}_N\) be a regular polygon of area \(\pi\) with \( N \geq 3\) sides. In this paper under review, the authors study the behavior of the Dirichlet eigenvalues \(\lambda_k(\mathcal{P}_N)\) as \(N\) goes to infinity. More precisely, they show that there exists a sequence of polynomials \(C_n\in \mathfrak{Z}_n[\lambda]\), \(n\geq 1\) where \(\mathfrak{Z}_n\) is the space of multiple zeta values of weight \(n\), such that \[\frac{\lambda_k(\mathcal{P}_N)}{\lambda_k}\sim 1+\sum_{n=1}^\infty \frac{C_n(\lambda_k)}{N^n} \]whenever \(\lambda_k\) is a radially-symmetric Dirichlet eigenvalue of the unit disk.\N\NThe approach to prove the above result yields an explicit symbolic algorithm for computing the polynomials \(C_n\). For instance, the authors calculate \(C_n\) for \(n\leq 14\) to check their conjecture which asserts that the polynomial \(C_n(\lambda)\) belongs to the space of singlevalued multiple zeta values of weight \(n\).
reviewed by: Sami Omar
Mathematics Subject Classification ID: 11G55
Mathematics Subject Classification ID: 11M32
Mathematics Subject Classification ID: 35P15
zbMATH DE Number: 7867909
zbMATH Keywords: Dirichlet eigenvalues
zbMATH Keywords: regular polygons
zbMATH Keywords: multiple zeta values
zbMATH Keywords: asymptotics
MaRDI profile type: Publication
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DOI: 10.1016/J.JMAA.2024.128460
description: scientific article; zbMATH DE number 7867909