Automorphic function: Difference between revisions

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{{Short description|Mathematical function on a space that is invariant under the action of some group}}

In mathematics, an '''automorphic function''' is a function on a space that is invariant under the [[Group action (mathematics)|action]] of some [[group (mathematics)|group]], in other words a function on the [[Quotient space (topology)|quotient space]]. Often the space is a [[complex manifold]] and the group is a [[discrete group]].

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==Examples==

*[[{{annotated link|Kleinian group]]}}

*[[{{annotated link|Elliptic modular function]]}}

*[[{{annotated link|Modular function]]}}

*{{annotated link|Complex torus}}

==References==

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*{{springer|id=a/a014160|author=A.N. Parshin|title=Automorphic Form}}

*{{eom|id=a/a014170|first=A.N. |last=Andrianov|first2= A.N. |last2=Parshin|title=Automorphic Function}}

*{{Citation | last1=Ford | first1=Lester R. |authorlink=Lester R. Ford| title=Automorphic functions | url=https://books.google.com/books?id=aqPvo173YIIC | publisher___location=New York,|publisher= McGraw-Hill | isbn=978-0-8218-3741-2 | jfm=55.0810.04 | year=1929}}

*{{Citation | last1=Fricke | first1=Robert | last2=Klein | first2=Felix |authorlink1=Robert Fricke|authorlink2= Felix Klein| title=Vorlesungen über die Theorie der automorphen Functionen.|volume Erster= Band;I. Die gruppentheoretischen Grundlagen. | url=https://archive.org/details/vorlesungenber01fricuoft | ___location=Leipzig|publisher=Leipzig: B. G. Teubner | language=German | isbn=978-1-4297-0551-6 | jfm=28.0334.01 | year=1897}}

*{{Citation | last1=Fricke | first1=Robert | last2=Klein | first2=Felix | title=Vorlesungen über die Theorie der automorphen Functionen. Zweiter Band: Die funktionentheoretischen Ausführungen und die Anwendungen. 1. Lieferung: Engere Theorie der automorphen Funktionen. | url=https://archive.org/details/vorlesungenber02fricuoft | ___location=Leipzig|publisher=Leipzig: B. G. Teubner. | language=German | isbn=978-1-4297-0552-3 | jfm=32.0430.01 | year=1912}}

[[Category:Automorphic forms]]