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Riemann was born on 17 September 1826 in Breselenz, a village near Dannenberg in the Kingdom of Hanover.His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor in Breselenz who fought in the Napoleonic Wars.
Riemann knew that the non-trivial zeros of the zeta function were symmetrically distributed about the line s = 1/2 + it, and he knew that all of its non-trivial zeros must lie in the range 0 ≤ Re(s) ≤ 1. He checked that a few of the zeros lay on the critical line with real part 1/2 and suggested that they all do; this is the Riemann hypothesis.
The German mathematician Bernhard Riemann (1826–1866) is the eponym of many things ... Riemann curvature tensor also called Riemann tensor; Riemann tensor (general ...
Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugural lecture "Ueber die Hypothesen, welche der Geometrie zu Grunde liegen" ("On the Hypotheses on which Geometry is Based"). [1] It is a very broad and abstract generalization of the differential geometry of surfaces in R 3.
The article "Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse" (usual English translation: "On the Number of Primes Less Than a Given Magnitude") is a seminal 9-page paper by Bernhard Riemann published in the November 1859 edition of the Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin.
In mathematics, the Riemann series theorem, also called the Riemann rearrangement theorem, named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series of real numbers is conditionally convergent, then its terms can be arranged in a permutation so that the new series converges to an arbitrary real number, and rearranged such that the new series diverges.
Riemannian manifolds and Riemann surfaces are named after Bernhard Riemann. In 1857, Riemann introduced the concept of Riemann surfaces as part of a study of the process of analytic continuation; Riemann surfaces are now recognized as one-dimensional complex manifolds. He also furthered the study of abelian and other multi-variable complex ...
Riemannian manifolds are named after German mathematician Bernhard Riemann, who first conceptualized them. Formally, a Riemannian metric (or just a metric) on a smooth manifold is a choice of inner product for each tangent space of the manifold. A Riemannian manifold is a smooth manifold together with a Riemannian metric.
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