Phrase Hound found 22 phrases and 2 compound words that contain riemann. The most common are listed below. Open riemann in the live search for definitions, filters, and the full list.
Phrases 22
- Riemann zeta functionThe function ζ defined by the Dirichlet series ζ(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic …
- Riemann hypothesisThe conjecture that the zeros of the Riemann zeta function exist only at the negative even integers and certain complex numbers whose real part is ½.
- Riemann surfaceA one-dimensional complex manifold; a generalization of the complex plane.
- Riemann sphereThe complex numbers extended with the number ∞; the complex plane (representation of the complex numbers as a Euclidean plane) extended with a single idealised point at infinity and consequently homeomorphic to a sphere in 3-dimensional …
- Riemann spaceA subset of Euclidean space in which tensors are used to describe distance, angle, and curvature
- Riemann integralA type of integral whose computation involves dividing the interval of integration into smaller sub-intervals, summing sample values of the integrand inside those sub-intervals multiplied by their lengths, and letting the number of …
- Riemann sumA certain kind of approximation of an integral by a finite sum that is calculated by dividing the interval of integration into smaller sub-intervals and summing sample values of the integrand inside those sub-intervals multiplied by their …
- Riemann-Roch theoremAn important theorem in complex analysis and algebraic geometry for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles.
- Riemann-Lebesgue lemmaA lemma, of importance in harmonic analysis and asymptotic analysis, stating that the Fourier transform or Laplace transform of an L1 function vanishes at infinity.
- Riemann surfacesplural of Riemann surface: A one-dimensional complex manifold; a generalization of the complex plane.
- Riemann-Stieltjes integralA generalization of the Riemann integral, serving as a precursor of the Lebesgue integral and a means of unifying equivalent forms of statistical theorems that apply to discrete and continuous probability.
- Riemann-Stieltjes integralsplural of Riemann-Stieltjes integral: A generalization of the Riemann integral, serving as a precursor of the Lebesgue integral and a means of unifying equivalent forms of statistical theorems that apply to discrete and continuous …
- Grothendieck-Riemann-Roch theoremAn important generalization of the Hirzebruch-Riemann-Roch theorem about complex manifolds.
- Hirzebruch-Riemann-Roch theoremA result generalizing the classical Riemann-Roch theorem on Riemann surfaces to all complex algebraic varieties of higher dimensions.
- Cauchy-Riemann equationGiven a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be …
- Cauchy-Riemann equationsplural of Cauchy-Riemann equation: Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the …
- Zariski-Riemann spaceA locally ringed space of a subring k of a field K, whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve.
- Riemann integralsplural of Riemann integral: A type of integral whose computation involves dividing the interval of integration into smaller sub-intervals, summing sample values of the integrand inside those sub-intervals multiplied by their lengths, and …
- Riemann spacesplural of Riemann space: A subset of Euclidean space in which tensors are used to describe distance, angle, and curvature
- Riemann spheresplural of Riemann sphere: The complex numbers extended with the number ∞; the complex plane (representation of the complex numbers as a Euclidean plane) extended with a single idealised point at infinity and consequently homeomorphic to a …
- Riemann zeta functionsplural of Riemann zeta function: The function ζ defined by the Dirichlet series ζ(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said …
- Zariski-Riemann spacesplural of Zariski-Riemann space: A locally ringed space of a subring k of a field K, whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve.
Compound words 2
- RiemannianOf or relating to the work, or theory developed from the work, of German mathematician Bernhard Riemann, especially to Riemannian manifolds and Riemannian geometry.
- RiemanneanAlternative form of Riemannian: Of or relating to the work, or theory developed from the work, of German mathematician Bernhard Riemann, especially to Riemannian manifolds and Riemannian geometry.