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- Z_function abstract "In mathematics, the Z-function is a function used for studying theRiemann zeta-function along the critical line where the real part of 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 byIt 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.".
- Z_function thumbnail Riemann_Siegel_Z_1.jpg?width=300.
- Z_function wikiPageExternalLink RiemannSiegelZ.
- Z_function wikiPageID "1415146".
- Z_function wikiPageRevisionID "580941896".
- Z_function hasPhotoCollection Z_function.
- Z_function title "Riemann-Siegel Functions".
- Z_function urlname "Riemann-SiegelFunctions".
- Z_function subject Category:Zeta_and_L-functions.
- Z_function comment "In mathematics, the Z-function is a function used for studying theRiemann zeta-function along the critical line where the real part of 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.".
- Z_function label "Función Z".
- Z_function label "Z function".
- Z_function sameAs Función_Z.
- Z_function sameAs m.04_p11.
- Z_function sameAs Q8063364.
- Z_function sameAs Q8063364.
- Z_function wasDerivedFrom Z_function?oldid=580941896.
- Z_function depiction Riemann_Siegel_Z_1.jpg.
- Z_function isPrimaryTopicOf Z_function.
