| dbo:abstract |
In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function on the m-fold product of upper half-planes satisfying a certain kind of functional equation. (en) En mathématiques, une forme modulaire de Hilbert est une généralisation des formes modulaires aux fonctions de deux variables ou plus. C'est une fonction analytique sur le produit de m demi-plans supérieurs satisfaisant un certain type d'équation fonctionnelle. (fr) Inom matematiken är en Hilbert-modulär form en generalisering av modulära former till funktioner av två eller flera variabler. Den är en (komplex) analytisk funktion som satisfierar en viss slags funktionalekvation. På samma sätt som vanliga modulära former innehåller aritmetisk information relaterad till elliptiska kurvor, innehåller Hilbert-modulära former information om högredimensionella abelska varieteter. (sv) 在數學中，希爾伯特模形式是一類自守形式，對應於全實域 及相應的群 。這可以視作模形式的一種多變元推廣。當 時，我們回到模形式的定義。 (zh) |
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dbr:Totally_real_number_field dbr:David_Hilbert dbr:Ring_of_integers dbr:Analytic_function dbr:Mathematics dbr:Modular_form dbr:Complex_manifold dbr:Functional_equation dbr:Eberhard_Freitag dbr:Erich_Hecke dbr:Otto_Blumenthal dbr:Upper_half-plane dbc:Automorphic_forms dbr:Habilitationssschrift dbr:Siegel_modular_form dbr:Hilbert_modular_surface dbr:Göttingen_University dbr:Real_embedding dbr:Real_quadratic_field dbr:Koecher's_principle dbr:Arxiv:math/0609763 dbr:Paul_B._Garrett |
| dbp:date |
August 2015 (en) |
| dbp:reason |
Hilbert MFs are not Siegel MFs; normal MFs are Hilbert MFs too (en) |
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dbt:Dubious dbt:ISBN dbt:Short_description |
| dct:subject |
dbc:Automorphic_forms |
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| rdfs:comment |
In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function on the m-fold product of upper half-planes satisfying a certain kind of functional equation. (en) En mathématiques, une forme modulaire de Hilbert est une généralisation des formes modulaires aux fonctions de deux variables ou plus. C'est une fonction analytique sur le produit de m demi-plans supérieurs satisfaisant un certain type d'équation fonctionnelle. (fr) Inom matematiken är en Hilbert-modulär form en generalisering av modulära former till funktioner av två eller flera variabler. Den är en (komplex) analytisk funktion som satisfierar en viss slags funktionalekvation. På samma sätt som vanliga modulära former innehåller aritmetisk information relaterad till elliptiska kurvor, innehåller Hilbert-modulära former information om högredimensionella abelska varieteter. (sv) 在數學中，希爾伯特模形式是一類自守形式，對應於全實域 及相應的群 。這可以視作模形式的一種多變元推廣。當 時，我們回到模形式的定義。 (zh) |
| rdfs:label |
Forme modulaire de Hilbert (fr) Hilbert modular form (en) Hilbert-modulär form (sv) 希爾伯特模形式 (zh) |
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