Maass wave form

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In mathematics, a Maass wave form or Maass 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 Hans Maass in Maass (1949).


A Maass wave form is defined to be a continuous complex-valued function f of x + iy in the upper half plane satisfying the following conditions:

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

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