About: Chowla–Mordell theorem

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In mathematics, the Chowla–Mordell theorem is a result in number theory determining cases where a Gauss sum is the square root of a prime number, multiplied by a root of unity. It was proved and published independently by Sarvadaman Chowla and Louis Mordell, around 1951. In detail, if is a prime number, a nontrivial Dirichlet character modulo , and where is a primitive -th root of unity in the complex numbers, then

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rdfs:label	Chowla–Mordell theorem (en) Théorème de Chowla-Mordell (fr)
rdfs:comment	In mathematics, the Chowla–Mordell theorem is a result in number theory determining cases where a Gauss sum is the square root of a prime number, multiplied by a root of unity. It was proved and published independently by Sarvadaman Chowla and Louis Mordell, around 1951. In detail, if is a prime number, a nontrivial Dirichlet character modulo , and where is a primitive -th root of unity in the complex numbers, then (en) En mathématiques, le théorème de Chowla-Mordell est un résultat de la théorie des nombres déterminant les cas où une somme de Gauss est la racine carrée d'un nombre premier, multipliée par une racine de l'unité. Il fut démontré et publié indépendamment par Sarvadaman Chowla et Louis Mordell, vers 1951. En détail, si p est un nombre premier, un caractère de Dirichlet non trivial modulo p, et où est une racine primitive p-ième de l'unité dans les nombres complexes, alors le quotient (fr)
dcterms:subject	Theorems in number theory Cyclotomic fields Zeta and L-functions
Wikipage page ID	595896 (xsd:integer)
Wikipage revision ID	962520018 (xsd:integer)
Link from a Wikipage to another Wikipage	Carl Friedrich Gauss Root of unity Sarvadaman Chowla Theorems in number theory Complex number Mathematics Gauss sum Modulo operation Cyclotomic fields Functional equation (L-function) Bruce C. Berndt Zeta and L-functions Number theory Dirichlet character Prime number Square root Quadratic residue symbol Louis Mordell
sameAs	Chowla–Mordell theorem Chowla–Mordell theorem Chowla–Mordell theorem Chowla–Mordell theorem
dbp:wikiPageUsesTemplate	dbt:Short_description
Link from a Wikipa... related subject.	Cyclotomic unit
has abstract	In mathematics, the Chowla–Mordell theorem is a result in number theory determining cases where a Gauss sum is the square root of a prime number, multiplied by a root of unity. It was proved and published independently by Sarvadaman Chowla and Louis Mordell, around 1951. In detail, if is a prime number, a nontrivial Dirichlet character modulo , and where is a primitive -th root of unity in the complex numbers, then is a root of unity if and only if is the quadratic residue symbol modulo . The 'if' part was known to Gauss: the contribution of Chowla and Mordell was the 'only if' direction. The ratio in the theorem occurs in the functional equation of L-functions. (en) En mathématiques, le théorème de Chowla-Mordell est un résultat de la théorie des nombres déterminant les cas où une somme de Gauss est la racine carrée d'un nombre premier, multipliée par une racine de l'unité. Il fut démontré et publié indépendamment par Sarvadaman Chowla et Louis Mordell, vers 1951. En détail, si p est un nombre premier, un caractère de Dirichlet non trivial modulo p, et où est une racine primitive p-ième de l'unité dans les nombres complexes, alors le quotient est une racine de l'unité si et seulement si est le symbole de Legendre modulo p. Le premier « si » était connu de Gauss : la contribution de Chowla et Mordell fut la direction du « seulement si ». Le quotient ci-dessus apparaît dans l'équation fonctionnelle des fonctions L. (fr)
prov:wasDerivedFrom	wikipedia-en:Chowla–Mordell_theorem?oldid=962520018&ns=0
page length (characters) of wiki page	1429 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Chowla–Mordell_theorem
is Link from a Wikipage to another Wikipage of	Sarvadaman Chowla Chowla-Mordell theorem Gauss sum Louis J. Mordell List of theorems
is Wikipage redirect of	Chowla-Mordell theorem
is known for of	Louis J. Mordell
is known for of	Louis J. Mordell
is foaf:primaryTopic of	wikipedia-en:Chowla–Mordell_theorem

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