Local zeta function
In number theory, the local zeta function Z(V, s) (sometimes called the congruent zeta function) is defined as where Nm is the number of points of V defined over the finite field extension Fqm of Fq, and V is a non-singular n-dimensional projective algebraic variety over the field Fq with q elements. Making the variable transformation u = q−s, gives as the formal power series in the variable . Equivalently, the local zeta function is sometimes defined as follows:
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Alexander GrothendieckArithmetic geometryArithmetic of abelian varietiesArtin–Mazur zeta functionBernard DworkCharacter sumChevalley–Warning theoremConjectureDiagonal formDiophantine geometryDwork familyEichler–Shimura congruence relationElliptic curveExplicit formulae for L-functionsField with one elementFunctional equation (L-function)Gaussian periodGlobal fieldGlossary of arithmetic and diophantine geometryGoro ShimuraHarold DavenportHasse's theorem on elliptic curvesHasse–Weil zeta functionHasse–Witt matrixHelmut HasseJacobi sumKloosterman sumList of number theory topicsList of things named after Bernhard RiemannList of zeta functionsLocalLocal zeta-functionMotive (algebraic geometry)Motivic zeta functionOscar ZariskiPseudo algebraically closed fieldRiemann hypothesisRiemann hypothesis for curves over finite fieldsSubgroup growthSéminaire Nicolas Bourbaki
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Local zeta function
In number theory, the local zeta function Z(V, s) (sometimes called the congruent zeta function) is defined as where Nm is the number of points of V defined over the finite field extension Fqm of Fq, and V is a non-singular n-dimensional projective algebraic variety over the field Fq with q elements. Making the variable transformation u = q−s, gives as the formal power series in the variable . Equivalently, the local zeta function is sometimes defined as follows:
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En la teoría de números, una f ...... extensión de cuerpos Fk de F.
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En matemàtiques, en la teoria ...... nsió de cossos de grau de de .
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En mathématiques et dans la th ...... t a priori une série formelle.
@fr
In number theory, the local ze ...... in the degree m extension Fqm.
@en
Na teoria dos números, uma fun ...... em extensão de campos Fk de F.
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Stel dat V een n-dimensionale ...... ad uitbreiding Fm definiërend.
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Конгруэнц-дзета-функция — прот ...... ствует аналог гипотезы Римана.
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数学において、q 個の元をもつ有限体 Fq 上で定義された非 ...... 、Z(V, u) の対数微分となるような関数とも定義できる。
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En la teoría de números, una f ...... extensión de cuerpos Fk de F.
@es
En matemàtiques, en la teoria ...... defineix de la següent manera:
@ca
En mathématiques et dans la th ...... réer la fonction génératrice .
@fr
In number theory, the local ze ...... sometimes defined as follows:
@en
Na teoria dos números, uma fun ...... em extensão de campos Fk de F.
@pt
Stel dat V een n-dimensionale ...... functie soms gedefinieerd als:
@nl
Конгруэнц-дзета-функция — прот ...... ствует аналог гипотезы Римана.
@ru
数学において、q 個の元をもつ有限体 Fq 上で定義された非 ...... 、Z(V, u) の対数微分となるような関数とも定義できる。
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Fonction zêta locale
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Funció zeta local
@ca
Función zeta local
@es
Função zeta local
@pt
Local zeta function
@en
Lokale zèta-functie
@nl
Локальная дзета-функция
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合同ゼータ関数
@ja
국소 제타 함수
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