About: Quadratic Gauss sum

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In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients given by a quadratic character; for a general character, one obtains a more general Gauss sum. These objects are named after Carl Friedrich Gauss, who studied them extensively and applied them to quadratic, cubic, and biquadratic reciprocity laws.

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rdfs:label	Somme quadratique de Gauss (fr) Quadratic Gauss sum (en) Soma quadrática de Gauss (pt) Kvadratisk Gaussumma (sv)
rdfs:comment	En théorie des nombres, une somme quadratique de Gauss est une certaine somme finie de racines de l'unité. Une somme quadratique de Gauss peut être interprétée comme une combinaison linéaire des valeurs de la fonction exponentielle complexe avec des coefficients donnés par un caractère quadratique ; pour un caractère général, on obtient une somme de Gauss plus générale. Ces objets sont nommés d'après Carl Friedrich Gauss, qui les a étudiés longuement et les a appliqués aux lois de réciprocité quadratique, cubique et (en). (fr) In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients given by a quadratic character; for a general character, one obtains a more general Gauss sum. These objects are named after Carl Friedrich Gauss, who studied them extensively and applied them to quadratic, cubic, and biquadratic reciprocity laws. (en) Na teoria dos números, as somas quadráticas de Gauss são certas somas finitas de raízes de unidade. Uma soma de Gauss quadrática pode ser interpretada como uma combinação linear dos valores da função exponencial complexa com coeficientes dados por um caractere quadrático; para um caráter geral, se obtém uma soma de Gauss mais geral. Esses objetos são nomeados em homenagem a Carl Friedrich Gauss, que os estudou extensivamente e os aplicou às leis de reciprocidade quadrática, cúbica e biquadrática. (pt) Inom talteori är en kvadratisk Gaussumma en viss ändlig summa av enhetsrötter. Summan är uppkallad efter Carl Friedrich Gauss som studerade dem och använde dem till kvadratiska, kubiska och reciprocitetslagar. (sv)
dcterms:subject	Cyclotomic fields
Wikipage page ID	595898 (xsd:integer)
Wikipage revision ID	1099642571 (xsd:integer)
Link from a Wikipage to another Wikipage	Carl Friedrich Gauss Multiplicative function Peter Gustav Lejeune Dirichlet Cubic reciprocity Jacobi symbol Gaussian period Gauss sum Greatest common divisor Leopold Kronecker Cyclotomic fields Completing the square Kummer sum Landsberg–Schaar relation Algebraic integer Cyclotomic field Exponential function Number theory Biquadratic reciprocity Quadratic reciprocity Issai Schur Prime number Chinese remainder theorem Hensel's lemma Square-free integer Natural numbers Proofs of quadratic reciprocity Primitive nth root of unity Residue class Geometric sum
sameAs	Quadratic Gauss sum Quadratic Gauss sum Quadratic Gauss sum Quadratic Gauss sum Quadratic Gauss sum Quadratic Gauss sum Quadratic Gauss sum Quadratic Gauss sum
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has abstract	En théorie des nombres, une somme quadratique de Gauss est une certaine somme finie de racines de l'unité. Une somme quadratique de Gauss peut être interprétée comme une combinaison linéaire des valeurs de la fonction exponentielle complexe avec des coefficients donnés par un caractère quadratique ; pour un caractère général, on obtient une somme de Gauss plus générale. Ces objets sont nommés d'après Carl Friedrich Gauss, qui les a étudiés longuement et les a appliqués aux lois de réciprocité quadratique, cubique et (en). (fr) In number theory, quadratic Gauss sums are certain finite sums of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients given by a quadratic character; for a general character, one obtains a more general Gauss sum. These objects are named after Carl Friedrich Gauss, who studied them extensively and applied them to quadratic, cubic, and biquadratic reciprocity laws. (en) Na teoria dos números, as somas quadráticas de Gauss são certas somas finitas de raízes de unidade. Uma soma de Gauss quadrática pode ser interpretada como uma combinação linear dos valores da função exponencial complexa com coeficientes dados por um caractere quadrático; para um caráter geral, se obtém uma soma de Gauss mais geral. Esses objetos são nomeados em homenagem a Carl Friedrich Gauss, que os estudou extensivamente e os aplicou às leis de reciprocidade quadrática, cúbica e biquadrática. (pt) Inom talteori är en kvadratisk Gaussumma en viss ändlig summa av enhetsrötter. Summan är uppkallad efter Carl Friedrich Gauss som studerade dem och använde dem till kvadratiska, kubiska och reciprocitetslagar. (sv)
gold:hypernym	Sums
prov:wasDerivedFrom	wikipedia-en:Quadratic_Gauss_sum?oldid=1099642571&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:Quadratic_Gauss_sum
is Link from a Wikipage to another Wikipage of	Riemann hypothesis Cubic reciprocity Gauss sum Landsberg–Schaar relation Legendre symbol List of things named after Carl Friedrich Gauss Exponential sum Paley graph Proofs of quadratic reciprocity
is foaf:primaryTopic of	wikipedia-en:Quadratic_Gauss_sum

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