Maass wave form
Complex-valued smooth functions of the upper half plane (harmonic analysis topic) / From Wikipedia, the free encyclopedia
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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 modular forms, Maass forms need not be holomorphic. They were studied first by Hans Maass in 1949.
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