In mathematics, a Maass wave form
is a function on the upper half plane
that transforms like a modular form
but need not be holomorphic
. They were first studied by Maass .
A Maass wave form is defined to be a continuous complex-valued function f
of τ = x
in the upper half plane satisfying the following conditions:
- f is invariant under the action of the group SL2(Z) on the upper half plane.
- f is an eigenvector of the Laplacian operator
- f is rapidly decreasing at cusps of SL2(Z).