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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 . ==Definition== Let ''k'' be a half-integer, ''s'' be a complex number, and Γ be a discrete subgroup of SL2(R). A Maass form of weight ''k'' for Γ with Laplace eigenvalue ''s'' is a smooth function from the upper half-plane to the complex numbers satisfying the following conditions: *For all and all , we have . *We have , where is the weight ''k'' hyperbolic laplacian defined as . *The function ''f'' is of at most polynomial growth at cusps. A weak Maass wave form is defined similarly but with the third condition replaced by "The function ''f'' has at most linear exponential growth at cusps". Moreover, f is said to be harmonic if it is annihilated by the Laplacian operator. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maass wave form」の詳細全文を読む スポンサード リンク
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