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- Factor_of_automorphy abstract "In mathematics, the notion of factor of automorphy arises for a group acting on a complex-analytic manifold. Suppose a group acts on a complex-analytic manifold . Then, also acts on the space of holomorphic functions from to the complex numbers. A function is termed an automorphic form if the following holds: where is an everywhere nonzero holomorphic function. Equivalently, an automorphic form is a function whose divisor is invariant under the action of .The factor of automorphy for the automorphic form is the function . An automorphic function is an automorphic form for which is the identity.Some facts about factors of automorphy: Every factor of automorphy is a cocycle for the action of on the multiplicative group of everywhere nonzero holomorphic functions. The factor of automorphy is a coboundary if and only if it arises from an everywhere nonzero automorphic form. For a given factor of automorphy, the space of automorphic forms is a vector space. The pointwise product of two automorphic forms is an automorphic form corresponding to the product of the corresponding factors of automorphy.Relation between factors of automorphy and other notions: Let be a lattice in a Lie group . Then, a factor of automorphy for corresponds to a line bundle on the quotient group . Further, the automorphic forms for a given factor of automorphy correspond to sections of the corresponding line bundle.The specific case of a subgroup of SL(2, R), acting on the upper half-plane, is treated in the article on automorphic factors.".
- Factor_of_automorphy wikiPageID "8200885".
- Factor_of_automorphy wikiPageRevisionID "596522182".
- Factor_of_automorphy author "A.N. Andrianov, A.N. Parshin".
- Factor_of_automorphy author "A.N. Parshin".
- Factor_of_automorphy hasPhotoCollection Factor_of_automorphy.
- Factor_of_automorphy id "a/a014160".
- Factor_of_automorphy id "a/a014170".
- Factor_of_automorphy title "Automorphic Form".
- Factor_of_automorphy title "Automorphic Function".
- Factor_of_automorphy subject Category:Automorphic_forms.
- Factor_of_automorphy type Abstraction100002137.
- Factor_of_automorphy type AutomorphicForms.
- Factor_of_automorphy type Form106290637.
- Factor_of_automorphy type LanguageUnit106284225.
- Factor_of_automorphy type Part113809207.
- Factor_of_automorphy type Relation100031921.
- Factor_of_automorphy type Word106286395.
- Factor_of_automorphy comment "In mathematics, the notion of factor of automorphy arises for a group acting on a complex-analytic manifold. Suppose a group acts on a complex-analytic manifold . Then, also acts on the space of holomorphic functions from to the complex numbers. A function is termed an automorphic form if the following holds: where is an everywhere nonzero holomorphic function.".
- Factor_of_automorphy label "Factor of automorphy".
- Factor_of_automorphy label "Fator de automorfia".
- Factor_of_automorphy label "Автоморфная функция".
- Factor_of_automorphy label "保型因子".
- Factor_of_automorphy sameAs 保型因子.
- Factor_of_automorphy sameAs Fator_de_automorfia.
- Factor_of_automorphy sameAs m.026vz7m.
- Factor_of_automorphy sameAs Q1985904.
- Factor_of_automorphy sameAs Q1985904.
- Factor_of_automorphy sameAs Factor_of_automorphy.
- Factor_of_automorphy wasDerivedFrom Factor_of_automorphy?oldid=596522182.
- Factor_of_automorphy isPrimaryTopicOf Factor_of_automorphy.