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In mathematics, the Z function is a function used for studying the Riemann zeta function along the critical line where the argument is one-half. It is also called the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined in terms of the Riemann–Siegel theta function and the Riemann zeta function by

Attributes	Values
rdfs:label	Función Z (es) Z function (en) Z-funktionen (sv)
rdfs:comment	En matemática, la función Z es una función usada para el estudio de lafunción zeta de Riemann a lo largo de la recta crítica, donde la parte real del argumento es 1/2. Es también llamada función Z de Riemann-Siegel o función zeta de Hardy.Ésta puede ser definida en términos de la y de la función zeta de Riemann como: (es) Inom matematiken är Z-funktionen en speciell funktion som används då man studerar Riemanns zetafunktion vid den kritiska linjen där den reella delen av argumentet är en halv. Den är även känd som Riemann-Siegels Z-funktion, Riemann-Siegels zetafunktion, Hardys funktion, Hardys Z-funktion och Hardys zetafunktion. Den kan definieras med hjälp av Riemann–Siegels thetafunktion och Riemanns zetafunktion som (sv) In mathematics, the Z function is a function used for studying the Riemann zeta function along the critical line where the argument is one-half. It is also called the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined in terms of the Riemann–Siegel theta function and the Riemann zeta function by (en)
foaf:depiction
dct:subject	Zeta and L-functions
Wikipage page ID	1415146 (xsd:integer)
Wikipage revision ID	1059073781 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Hardy-Littlewood zeta-function conjectures Riemann hypothesis Riemann zeta function Riemann–Siegel formula Mathematics Function (mathematics) G. H. Hardy Lindelöf Zeta and L-functions Oxford University Press Critical line theorem Root mean square Incomplete gamma function Real analytic function Riemann–Siegel theta function Springer-Verlag
Link from a Wikipage to an external page	http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/RiemannSiegelZ/ https://archive.org/details/asymptoticsmelli0000pari
sameAs	Z function Z function Z function Z function Z function Z function Z function
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Main dbt:MathWorld
thumbnail	wiki-commons:Special:FilePath/Z_function_in_the_complex_plane,_-5,_5.svg?width=300
title	Riemann–Siegel Functions (en)
urlname	Riemann-SiegelFunctions (en)
has abstract	En matemática, la función Z es una función usada para el estudio de lafunción zeta de Riemann a lo largo de la recta crítica, donde la parte real del argumento es 1/2. Es también llamada función Z de Riemann-Siegel o función zeta de Hardy.Ésta puede ser definida en términos de la y de la función zeta de Riemann como: (es) In mathematics, the Z function is a function used for studying the Riemann zeta function along the critical line where the argument is one-half. It is also called the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined in terms of the Riemann–Siegel theta function and the Riemann zeta function by It follows from the functional equation of the Riemann zeta function that the Z function is real for real values of t. It is an even function, and real analytic for real values. It follows from the fact that the Riemann-Siegel theta function and the Riemann zeta function are both holomorphic in the critical strip, where the imaginary part of t is between −1/2 and 1/2, that the Z function is holomorphic in the critical strip also. Moreover, the real zeros of Z(t) are precisely the zeros of the zeta function along the critical line, and complex zeros in the Z function critical strip correspond to zeros off the critical line of the Riemann zeta function in its critical strip. (en) Inom matematiken är Z-funktionen en speciell funktion som används då man studerar Riemanns zetafunktion vid den kritiska linjen där den reella delen av argumentet är en halv. Den är även känd som Riemann-Siegels Z-funktion, Riemann-Siegels zetafunktion, Hardys funktion, Hardys Z-funktion och Hardys zetafunktion. Den kan definieras med hjälp av Riemann–Siegels thetafunktion och Riemanns zetafunktion som (sv)
prov:wasDerivedFrom	wikipedia-en:Z_function?oldid=1059073781&ns=0
page length (characters) of wiki page	7772 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Z_function
is Link from a Wikipage to another Wikipage of	Riemann hypothesis Riemann zeta function Riemann–Siegel formula G. H. Hardy Turing's method Riemann–Siegel theta function Hardy function Z-function
is Wikipage redirect of	Hardy function Z-function
is foaf:primaryTopic of	wikipedia-en:Z_function

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