Wave form

Maass wave form

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 .

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^2left(frac{partial^2}{partial x^2} + frac{partial^2}{partial y^2}right)
  • f is rapidly decreasing at cusps of SL2(Z).

See also

References

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