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In mathematics, a character sum is a sum of values of a Dirichlet character χ modulo N, taken over a given range of values of n. Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue modulo N. Character sums are often closely linked to exponential sums by the Gauss sums (this is like a finite Mellin transform). Assume χ is a nonprincipal Dirichlet character to the modulus N.

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rdf:type	yago:Abstraction100002137 yago:Attribute100024264 yago:Difference104748836 yago:Inequality104752221 yago:Quality104723816 yago:WikicatInequalities
rdfs:label	Character sum (en) Karaktersom (nl)
rdfs:comment	In mathematics, a character sum is a sum of values of a Dirichlet character χ modulo N, taken over a given range of values of n. Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue modulo N. Character sums are often closely linked to exponential sums by the Gauss sums (this is like a finite Mellin transform). Assume χ is a nonprincipal Dirichlet character to the modulus N. (en) In de analytische getaltheorie, een deelgebied van de wiskunde, is een karaktersom een som van waarden van een Dirichlet-karakter χ modulo N, genomen over een gegeven bereik van waarden van n. Dergelijke sommen zijn basaal in een aantal vragen, bijvoorbeeld in de verdeling van kwadratische residuen, en met name in het klassieke probleem van het vinden van een bovengrens voor het minst kwadratische niet-residu modulo N. Karaktersommen zijn vaak nauw verbonden met exponentiële sommen door de Gauss-sommen (dit is als een eindige Mellin-transformatie). (nl)
dcterms:subject	Analytic number theory
Wikipage page ID	2986034 (xsd:integer)
Wikipage revision ID	1121965580 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Prime Quadratic residues Mellin transform Jacobi symbol Conic section Mathematics Generalized Riemann hypothesis Genus (mathematics) Elliptic curve Gauss sum George Pólya Modular arithmetic André Weil Local zeta-function Mathematika Linear function Dirichlet character Legendre symbol Hyperelliptic curve Analytic number theory Big O notation Polynomial Exponential sum Hugh Montgomery (mathematician) Least quadratic non-residue I. M. Vinogradov Robert Charles Vaughan (mathematician)
Link from a Wikipage to an external page	https://deepblue.lib.umich.edu/bitstream/2027.42/46603/1/222_2005_Article_BF01390204.pdf https://web.archive.org/web/20050207212539/http:/planetmath.org/encyclopedia/PolyaVinogradovInequality.html
sameAs	Character sum Character sum Character sum Character sum
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:MathWorld dbt:Reflist dbt:Sfn dbt:Short_description
title	The Pólya–Vinogradov inequality (en)
urlname	Polya-VinogradovInequality (en)
has abstract	In mathematics, a character sum is a sum of values of a Dirichlet character χ modulo N, taken over a given range of values of n. Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue modulo N. Character sums are often closely linked to exponential sums by the Gauss sums (this is like a finite Mellin transform). Assume χ is a nonprincipal Dirichlet character to the modulus N. (en) In de analytische getaltheorie, een deelgebied van de wiskunde, is een karaktersom een som van waarden van een Dirichlet-karakter χ modulo N, genomen over een gegeven bereik van waarden van n. Dergelijke sommen zijn basaal in een aantal vragen, bijvoorbeeld in de verdeling van kwadratische residuen, en met name in het klassieke probleem van het vinden van een bovengrens voor het minst kwadratische niet-residu modulo N. Karaktersommen zijn vaak nauw verbonden met exponentiële sommen door de Gauss-sommen (dit is als een eindige Mellin-transformatie). (nl)
prov:wasDerivedFrom	wikipedia-en:Character_sum?oldid=1121965580&ns=0
page length (characters) of wiki page	5539 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Character_sum
is Link from a Wikipage to another Wikipage of	Roger Heath-Brown Jacobi sum Lillian Pierce Generalized Riemann hypothesis Pólya-Vinogradov inequality Quadratic residue Finite field Brewer sum Dirichlet character Exponential sum Polya-Vinogradov inequality Pólya–Vinogradov inequality Burgess bound
is Wikipage redirect of	Pólya-Vinogradov inequality Polya-Vinogradov inequality Pólya–Vinogradov inequality Burgess bound
is foaf:primaryTopic of	wikipedia-en:Character_sum

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