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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:## See also

## References

- f is invariant under the action of the group SL
_{2}(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 SL
_{2}(Z).

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Last updated on Tuesday September 23, 2008 at 13:07:34 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Tuesday September 23, 2008 at 13:07:34 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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