Maass wave form

Summary

A Maass wave form is a smooth function on the upper half-plane that is invariant under a congruence subgroup of the modular group. It is also an eigenfunction of the hyperbolic Laplace–Beltrami operator. It is the non-holomorphic counterpart of a modular form. Maass forms are basic examples of automorphic forms, and their eigenvalues are the subject of spectral theory and trace formulas.