4 papers
A Database of Modular Forms on Noncongruence Subgroups
David Berghaus, Hartmut Monien, Danylo Radchenko
We present a database of several hundred modular forms up to and including weight six on noncongruence subgroups of index . In addition, our database contains expressions…
Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry
David Berghaus, Robert Stephen Jones, Hartmut Monien +1
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 met…
On the computation of modular forms on noncongruence subgroups
David Berghaus, Hartmut Monien, Danylo Radchenko
We present two approaches that can be used to compute modular forms on noncongruence subgroups. The first approach uses Hejhal's method for which we improve the arbitrary precision…
On Dirichlet eigenvalues of regular polygons
David Berghaus, Bogdan Georgiev, Hartmut Monien +1
We prove that the first Dirichlet eigenvalue of a regular -gon of area has an asymptotic expansion of the form as , where $λ_…