On Dirichlet eigenvalues of regular polygons
| Autor: | Berghaus, David, Georgiev, Bogdan, Monien, Hartmut, Radchenko, Danylo |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $n\le14$. Comment: 15 pages |
| Databáze: | arXiv |
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