Riemann zeta function — ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): dark colors denote values close to zero and hue encodes the value s argument. The white spot at s = 1 is the pole of the zeta function; the black spots on the… … Wikipedia
Riemann hypothesis — The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011 … Wikipedia
Riemann sphere — The Riemann sphere can be visualized as the complex number plane wrapped around a sphere (by some form of stereographic projection – details are given below). In mathematics, the Riemann sphere (or extended complex plane), named after the 19th… … Wikipedia
Riemann–Roch theorem — In mathematics, specifically in complex analysis and algebraic geometry, the Riemann–Roch theorem is an important tool in the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates… … Wikipedia
Riemann–Roch theorem for surfaces — In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was first given by Castelnuovo (1896, 1897), after preliminary versions of it were found by… … Wikipedia
Riemann-Roch-Theorem — Der Satz von Riemann Roch (nach dem Mathematiker Bernhard Riemann und seinem Schüler Gustav Roch) ist eine zentrale Aussage der Theorie kompakter riemannscher Flächen. Er gibt an, wie viele linear unabhängige meromorphe Funktionen mit… … Deutsch Wikipedia
Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… … Wikipedia
Riemann curvature tensor — In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor is the most standard way to express curvature of Riemannian manifolds. It is one of many things named after Bernhard Riemann and Elwin… … Wikipedia
Riemann-Stieltjes integral — In mathematics, the Riemann Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. DefinitionThe Riemann Stieltjes integral of a real valued function f of a real variable with… … Wikipedia
Riemann'sche Hypothese — Die riemannsche Vermutung oder riemannsche Hypothese (nach Bernhard Riemann) ist eine Annahme über die Nullstellen der riemannschen Zetafunktion. Sie besagt, dass alle nichttrivialen Nullstellen dieser komplexwertigen Funktion den Realteil ½… … Deutsch Wikipedia