• Corpus ID: 232092152

On Dirichlet eigenvalues of regular polygons

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

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