About: Ankeny–Artin–Chowla congruence

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In number theory, the Ankeny–Artin–Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla. It concerns the class number h of a real quadratic field of discriminant d > 0. If the fundamental unit of the field is with integers t and u, it expresses in another form for any prime number p > 2 that divides d. In case p > 3 it states that where and is the Dirichlet character for the quadratic field. For p = 3 there is a factor (1 + m) multiplying the LHS. Here represents the floor function of x. A related result is that if d=p is congruent to one mod four, then

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rdfs:label	Ankeny–Artin–Chowla congruence (en) Congruence d'Ankeny-Artin-Chowla (fr)
rdfs:comment	In number theory, the Ankeny–Artin–Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla. It concerns the class number h of a real quadratic field of discriminant d > 0. If the fundamental unit of the field is with integers t and u, it expresses in another form for any prime number p > 2 that divides d. In case p > 3 it states that where and is the Dirichlet character for the quadratic field. For p = 3 there is a factor (1 + m) multiplying the LHS. Here represents the floor function of x. A related result is that if d=p is congruent to one mod four, then (en) En théorie des nombres, la congruence d'Ankeny-Artin-Chowla est un résultat publié en 1951 par (en), Emil Artin et Sarvadaman Chowla. Elle concerne le nombre de classes h de l'anneau des entiers d'un corps quadratique réel de discriminant d > 0. Si l'unité fondamentale du corps est avec t et u entiers, elle exprime sous une autre forme la classe de congruence modulo p de pour tout nombre premier p > 2 qui divise d. Dans le cas p > 3, elle établit : représente la fonction partie entière de x. Un résultat relié est le suivant : où Bn est le n-ième nombre de Bernoulli. (fr)
dcterms:subject	Theorems in algebraic number theory
Wikipage page ID	534610 (xsd:integer)
Wikipage revision ID	961604706 (xsd:integer)
Link from a Wikipage to another Wikipage	Quadratic field Bernoulli number Annals of Mathematics Class number (number theory) Emil Artin Fundamental unit (number theory) Floor function Number theory Dirichlet character Prime number Theorems in algebraic number theory Discriminant Sides of an equation S. Chowla N. C. Ankeny
Link from a Wikipage to an external page	http://repository.ias.ac.in/8797/1/395.pdf
sameAs	Ankeny–Artin–Chowla congruence Ankeny–Artin–Chowla congruence Ankeny–Artin–Chowla congruence Ankeny–Artin–Chowla congruence
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Short_description dbt:Numtheory-stub
has abstract	In number theory, the Ankeny–Artin–Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla. It concerns the class number h of a real quadratic field of discriminant d > 0. If the fundamental unit of the field is with integers t and u, it expresses in another form for any prime number p > 2 that divides d. In case p > 3 it states that where and is the Dirichlet character for the quadratic field. For p = 3 there is a factor (1 + m) multiplying the LHS. Here represents the floor function of x. A related result is that if d=p is congruent to one mod four, then where Bn is the nth Bernoulli number. There are some generalisations of these basic results, in the papers of the authors. (en) En théorie des nombres, la congruence d'Ankeny-Artin-Chowla est un résultat publié en 1951 par (en), Emil Artin et Sarvadaman Chowla. Elle concerne le nombre de classes h de l'anneau des entiers d'un corps quadratique réel de discriminant d > 0. Si l'unité fondamentale du corps est avec t et u entiers, elle exprime sous une autre forme la classe de congruence modulo p de pour tout nombre premier p > 2 qui divise d. Dans le cas p > 3, elle établit : où et est le caractère de Dirichlet pour le corps quadratique. Pour p = 3, il existe un facteur (1 + m) multipliant le côté gauche de l'équation. Ici, représente la fonction partie entière de x. Un résultat relié est le suivant : où Bn est le n-ième nombre de Bernoulli. Il existe certaines généralisations de ces résultats de base dans les articles des auteurs. (fr)
prov:wasDerivedFrom	wikipedia-en:Ankeny–Artin–Chowla_congruence?oldid=961604706&ns=0
page length (characters) of wiki page	2061 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Ankeny–Artin–Chowla_congruence
is Link from a Wikipage to another Wikipage of	Sarvadaman Chowla Ankeny-Artin-Chowla theorem Ankeny–Artin–Chowla theorem Bernoulli number Ankeny-Artin-Chowla congruence Nesmith Ankeny List of things named after Emil Artin
is Wikipage redirect of	Ankeny-Artin-Chowla theorem Ankeny–Artin–Chowla theorem Ankeny-Artin-Chowla congruence
is foaf:primaryTopic of	wikipedia-en:Ankeny–Artin–Chowla_congruence

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