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  2. Riemann–Siegel formula - Wikipedia

    en.wikipedia.org/wiki/RiemannSiegel_formula

    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.

  3. Z function - Wikipedia

    en.wikipedia.org/wiki/Z_function

    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.

  4. Riemann zeta function - Wikipedia

    en.wikipedia.org/wiki/Riemann_zeta_function

    The Riemann zeta function ζ(z) plotted with domain coloring. [1] The pole at = and two zeros on the critical line.. The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (), is a mathematical function of a complex variable defined as () = = = + + + for ⁡ >, and its analytic continuation elsewhere.

  5. Carl Ludwig Siegel - Wikipedia

    en.wikipedia.org/wiki/Carl_Ludwig_Siegel

    Carl Ludwig Siegel (31 December 1896 – 4 April 1981) was a German mathematician specialising in analytic number theory.He is known for, amongst other things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation, Siegel's method, [1] Siegel's lemma and the Siegel mass formula for quadratic forms.

  6. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    6.2 (4,0) Riemann curvature tensor. 6.3 ... The variation formula computations above define the principal symbol of the mapping which sends a pseudo-Riemannian metric ...

  7. Bernhard Riemann - Wikipedia

    en.wikipedia.org/wiki/Bernhard_Riemann

    Georg Friedrich Bernhard Riemann (/ ˈ r iː m ɑː n /; [1] German: [ˈɡeːɔʁk ˈfʁiːdʁɪç ˈbɛʁnhaʁt ˈʁiːman] ⓘ; [2] [3] 17 September 1826 – 20 July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry.

  8. Riemann–Siegel theta function - Wikipedia

    en.wikipedia.org/wiki/RiemannSiegel_theta...

    In mathematics, the Riemann–Siegel theta function is defined in terms of the gamma function as = ⁡ ((+)) ⁡for real values of t.Here the argument is chosen in such a way that a continuous function is obtained and () = holds, i.e., in the same way that the principal branch of the log-gamma function is defined.

  9. Method of steepest descent - Wikipedia

    en.wikipedia.org/wiki/Method_of_steepest_descent

    In mathematics, the method of steepest descent or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms a contour integral in the complex plane to pass near a stationary point (saddle point), in roughly the direction of steepest descent or stationary phase.