Bob Jones

Summer 2016

This project presents the lowest 164,311 distinct eigenvalues (81,913 Dirichlet and 82,390 Neumann) of the Laplacian within the (unit-edged) regular pentagon. This list corresponds to all eigenvalues up to just over 1,000,000; with the highest eigenfunctions in this list having about 250 wavelengths across the regular pentagon.

- 100-digit eigenvalues (Refinement of Initial Sweep. Work In Progress)

- Initial GSVD sweep data. Has lists of approximate eigenvalues and Weyl counting plots for each symmetry tower.

- Weyl counting function and plots. Some details.

Plots of eigenfunctions corresponding to lowest 800 Dirichlet eigenvalues only. Very useful to see the dihedral symmetry classification into "ABCS".

- 8140 sixty-digit Dirichlet Eigenvalues up to $\lambda=10^5$ with relative error less than $10^{-60}$. (Aug 2018, Corrected)