Artin reciprocity law
The Artin reciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory. The term "reciprocity law" refers to a long line of more concrete number theoretic statements which it generalized, from the quadratic reciprocity law and the reciprocity laws of Eisenstein and Kummer to Hilbert's product formula for the norm symbol. Artin's result provided a partial solution to Hilbert's ninth problem.
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Adele ringAlgebraic number fieldAlgebraic number theoryArtinArtin's reciprocity theoremArtin L-functionArtin isomorphismArtin mapArtin reciprocityArtin reciprocity mapArtin reciprocity theoremArtin symbolArtin transfer (group theory)Class field theoryClass formationConductor (class field theory)Cubic reciprocityDefining modulusEisenstein reciprocityGalois moduleGenus characterGlobal Artin mapGlobal Artin symbolHecke characterHilbert's ninth problemHilbert symbolKronecker symbolLafforgue's theoremLanglands programLegendre symbolList of algebraic number theory topicsList of eponymous lawsList of things named after Emil ArtinLocal Artin mapLocal Artin symbolLocal Langlands conjecturesLocal symbolNikolai ChebotaryovNon-abelian class field theoryOctic reciprocity
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Artin reciprocity law
The Artin reciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory. The term "reciprocity law" refers to a long line of more concrete number theoretic statements which it generalized, from the quadratic reciprocity law and the reciprocity laws of Eisenstein and Kummer to Hilbert's product formula for the norm symbol. Artin's result provided a partial solution to Hilbert's ninth problem.
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Das Artinsche Reziprozitätsges ...... ch kann man es so formulieren:
@de
En mathématiques, la loi de ré ...... ces de la réciprocité d'Artin.
@fr
La Ley de reciprocidad de Arti ...... al noveno problema de Hilbert.
@es
The Artin reciprocity law, whi ...... on to Hilbert's ninth problem.
@en
アルティンの相互法則またはアルティン相互律（アルティンそうご ...... 法則である。アルティンの結果は、への部分的解答となっている。
@ja
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Das Artinsche Reziprozitätsges ...... man es wie folgt formulieren:
@de
En mathématiques, la loi de ré ...... els du programme de Langlands.
@fr
La Ley de reciprocidad de Arti ...... al noveno problema de Hilbert.
@es
The Artin reciprocity law, whi ...... on to Hilbert's ninth problem.
@en
アルティンの相互法則またはアルティン相互律（アルティンそうご ...... 法則である。アルティンの結果は、への部分的解答となっている。
@ja
label
Artin reciprocity law
@en
Artinsches Reziprozitätsgesetz
@de
Ley de reciprocidad de Artin
@es
Loi de réciprocité d'Artin
@fr
アルティン相互法則
@ja
아르틴 상호 법칙
@ko