# On Dirichlet eigenvalues of regular polygons

@inproceedings{Berghaus2021OnDE, title={On Dirichlet eigenvalues of regular polygons}, author={David Berghaus and Bogdan Georgiev and H. Monien and Danylo V. Radchenko}, year={2021} }

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≥3 Cn(λ1) N ) 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. We also explicitly compute these polynomials for all n ≤ 14.

## One Citation

### Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry

- MathematicsArXiv
- 2022

. We numerically compute the lowest Laplacian eigenvalues of several two-dimensional shapes with dihedral symmetry at arbitrary precision arithmetic. Our approach is based on the method of particular…

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