e/Automorphic form

Information
has gloss	eng: In mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps of several complex variables, of the theory of modular forms. It is in terms of a Lie group G, to generalise the groups SL2(R) or PSL2 (R) of modular forms, and a discrete group \Gamma \subset G, to generalise the modular group, or one of its congruence subgroups.
lexicalization	eng: Automorphic forms
lexicalization	eng: automorphic form
subclass of	(noun) the phonological or orthographic sound or appearance of a word that can be used to describe or identify something; "the inflected forms of a word can be represented by a stem and a list of inflections to be attached" word form, descriptor, signifier, form
has instance	e/Arthur Selberg trace formula
has instance	e/Arthur conjectures
has instance	e/Endoscopic group
has instance	e/Factor of automorphy
has instance	e/Hilbert modular form
has instance	e/Hilbert's twenty-second problem
has instance	e/Jacquet–Langlands correspondence
has instance	e/Kirillov model
has instance	e/Kleinian group
has instance	e/Langlands group
has instance	e/Local trace formula
has instance	e/Multiplicity-one theorem
has instance	e/Poincaré series (modular form)
has instance	e/Selberg trace formula
has instance	e/Shimura variety
has instance	e/Siegel upper half-space
has instance	e/Whittaker model

Meaning
Bosnian
lexicalization	bos: Automorfni oblici
Japanese
has gloss	jpn: 数学における一般的な意味での保型形式（ほけいけいしき、）は、モジュラー形式論における（一般には複素多変数の）解析函数を拡張するものである。リー群 G の言葉で言えば、モジュラー形式の群 SL2(R), PSL2(R) や離散群 Γ ⊂ G をモジュラー群またはその合同部分群に一般化するものである。
lexicalization	jpn: 保型形式
Dutch
lexicalization	nld: Automorfe vorm
Norwegian Nynorsk
lexicalization	nno: Automorfe former
Portuguese
has gloss	por: Em matemática, a noção geral de forma automórfica é a extensão a funções analíticas, talvez de múltiplas variáveis complexas, da teoria das formas modulares. É em termos de um grupo de Lie G, generalizar os grupos SL2(R) ou PSL2 (R) de formas modulares, e um grupo discreto \Gamma \in G, para generalizar o grupo modular, ou um de seus subgrupos congruentes. A formulação requer a noção geral de fator de automorfia j para \Gamma, a qual é o tipo de 1-cociclo na linguagem de co-homologia de grupo. Os valores de j podem ser números complexos, ou de fato matrizes complexas quadradas, correspondendo à possibilidade de valor de vetor das formas automórficas. A condição cociclo impostas sobre o fator de automorfia é alguma que possa ser rotineiramente checada, quando j é derivada de uma matriz Jacobiana, por significar a regra da cadeia.
lexicalization	por: forma automórfica
Chinese
has gloss	zho: 數學上所謂的自守形式，是一類特別的複變數函數，並在某個離散變換群下滿足由自守因子描述之變換規律。模形式與馬斯形式是其特例。由自守形式可定義自守表示，嚴格言之，自守表示並非尋常意義下的群表示，而是整體赫克代數上的模。
lexicalization	zho: 自守形式

Word:	(case sensitive)
Language:	(ISO 639-3 code, e.g. "eng" for English)

e/Automorphic form

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