Maass wave form

Share on Facebook Share on Twitter Email
Top

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 (1949).

Definition

A Maass wave form is defined to be a continuous complex-valued function f of τ = x + iy 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 -y^2\left(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}\right).
  • f is of at most polynomial growth at cusps of SL2(Z).

A weak Maass wave form is defined similarly but without the growth condition at cusps.

See also

References


Post a question - any question - to the WikiAnswers community:

Copyrights: