CC BY 4.0Berghaus, DavidDavidBerghausGeorgiev, BogdanBogdanGeorgievMonien, HartmutHartmutMonienRadchenko, Danylo V.Danylo V.Radchenko2024-08-062024-09-182024-08-062024-10-15https://doi.org/10.24406/h-472817https://publica.fraunhofer.de/handle/publica/47281710.1016/j.jmaa.2024.12846010.24406/h-4728172-s2.0-85192139132We 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[Formula presented]) 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 and conjecture that their coefficients lie in the space of single-valued multiple zeta values. We also explicitly compute these polynomials for all n≤14.enopen accessAsymptoticsDirichlet eigenvaluesMultiple zeta valuesRegular polygonsjournal article