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Concept information

mathematical physics > special function > Riemann zeta function > Riemann-Siegel formula
mathematical analysis > functional analysis > special function > Riemann zeta function > Riemann-Siegel formula
mathematical analysis > complex analysis > analytic function > Riemann zeta function > Riemann-Siegel formula
... > mathematical analysis > real analysis > real-valued function > analytic function > Riemann zeta function > Riemann-Siegel formula
... > number > number theory > analytic number theory > L-function > Riemann zeta function > Riemann-Siegel formula
... > mathematical analysis > complex analysis > meromorphic function > L-function > Riemann zeta function > Riemann-Siegel formula

Preferred term

Riemann-Siegel formula  

Definition

  • In mathematics, the Riemann–Siegel formula is an asymptotic formula for the error of the approximate functional equation of the Riemann zeta function, an approximation of the zeta function by a sum of two finite Dirichlet series. It was found by Siegel (1932) in unpublished manuscripts of Bernhard Riemann dating from the 1850s. Siegel derived it from the Riemann–Siegel integral formula, an expression for the zeta function involving contour integrals. It is often used to compute values of the Riemann–Siegel formula, sometimes in combination with the Odlyzko–Schönhage algorithm which speeds it up considerably. When used along the critical line, it is often useful to use it in a form where it becomes a formula for the Z function.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riemann%E2%80%93Siegel_formula)

Broader concept

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URI

http://data.loterre.fr/ark:/67375/PSR-JR31C2H3-1

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