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arXiv · 2103.01057

On Dirichlet eigenvalues of regular polygons

David Berghaus·Bogdan Georgiev·Hartmut Monien·Danylo Radchenko
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Abstract

We prove that the first Dirichlet eigenvalue of a regular $N$-gon of area $\pi$ has an asymptotic expansion of the form $\lambda_1(1+\sum_{n\ge3}C_n(\lambda_1)N^{-n})$ as $N\to\infty$, 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 $n$. We also explicitly compute these polynomials for all $n\le14$.

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David Berghaus, Bogdan Georgiev, Hartmut Monien, Danylo Radchenko. 2021-03-01. On Dirichlet eigenvalues of regular polygons. https://arxiv.org/abs/2103.01057

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