Category

Bernhard Riemann

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Bernhard Riemann

German mathematician (1826–1866)

Riemann hypothesis

conjecture in mathematics linked to the repartition of prime numbers

Riemann zeta function

analytic function

Riemann integral

basic type of integral in elementary calculus

Riemannian geometry

branch of differential geometry dealing with (generalized) Riemannian manifolds

Riemann surface

one-dimensional complex manifold

model of the extended complex plane plus a point at infinity

Cauchy–Riemann equations

system of linear partial differential equations characterizing holomorphic (complex differentiable) functions

Riemann curvature tensor

tensor field in general relativity and geometry

approximation technique in integral calculus

Riemann–Stieltjes integral

generalization of the Riemann integral where one integrates a function with respect to another function

pseudo-Riemannian manifold

smooth manifold equipped with nowhere degenerate (but not necessarily positive-definite) metric tensor

Riemann mapping theorem

theorem that any non-empty simply connected open proper subset of the complex plane is biholomorphic to the open unit disk

removable singularity

pole of order zero; a point at which a holomorphic function is undefined, but it is possible to redefine the function at that point in such a way that the resulting function is regular in a neighbourhood of that point

Generalized Riemann hypothesis

Various conjectures about the zeroes of some functions similar to the Riemann zeta function

Riemann series theorem

On the Number of Primes Less Than a Given Magnitude

scientific article by Bernhard Riemann

Riemann–Lebesgue lemma

lemma that the Fourier transform of an L¹ function vanishes at infinity

Riemann Xi function

simpler variant of the Riemann zeta function

Riemann–Roch theorem

theorem that the Euler characteristic of the sheaf cohomology of a holomorphic line bundle on a Riemann surface equals the degree of the bundle plus half of the Euler characteristic of the surface

local zeta function

function whose logarithmic derivative is a generating function for the number of solutions of a set of equations defined over a finite field

Riemann–Siegel theta function

mathematical term

Hirzebruch–Riemann–Roch theorem

on the Euler characteristic of a holomorphic vector bundle on a compact complex manifold

Riemann–Liouville integral

Integral transform

Riemann problem

mathematical problem

Riemann–Siegel formula

Mathematical formula

Grothendieck–Hirzebruch–Riemann–Roch theorem

Result in algebraic geometry

Riemann invariant

quantity that is constant along characteristic curves in a system of conservation equations

Riemann–von Mangoldt formula

Riemann's differential equation

generalization of the hypergeometric differential equation