hbeLabs.com

## Eigenvalue Problem in the Regular Pentagon

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.

1. 100-digit eigenvalues (Refinement of Initial Sweep. Work In Progress)

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

3. Weyl counting function and plots. Some details.

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

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