Automorphic forms

Maass wave form

In mathematics, Maass forms or Maass wave forms are studied in the theory of automorphic forms. Maass forms are complex-valued smooth functions of the upper half plane, which transform in a similar way under the operation of a discrete subgroup of as modular forms. They are Eigenforms of the hyperbolic Laplace Operator defined on and satisfy certain growth conditions at the cusps of a fundamental domain of . In contrast to the modular forms the Maass forms need not be holomorphic. They were studied first by Hans Maass in 1949. (Wikipedia).

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From playlist Mathematics

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Related pages

Real analytic Eisenstein series | SL2(R) | Upper half-plane | Modular form | Cusp form | Gamma function | Q.E.D. | Bessel function | Harmonic Maass form | Adele ring | Voronoi formula | Automorphic form | Identity theorem | Smoothness | Locally compact group | Mock modular form | Holomorphic function