riemann in English

noun

Georg Friedrich Bernhard Riemann (1826-66), German mathematician, founder of non-Euclidean geometry

Use "riemann" in a sentence

1. An introduction to the theory of the Riemann zeta-function.

2. The Riemann zeta function ζ(s) is used in many areas of mathematics.

3. A one-complex-dimensional manifold is called a Riemann surface.

4. 4 This, the Riemann curvature tensor, quantifies space-time curvature.

5. The Riemann hypothesis implies results about the distribution of prime numbers.

6. The Riemann hypothesis discusses zeros outside the region of convergence of this series and Euler product.

7. These theories depended on the properties of a function defined on Riemann surfaces.

8. Otherwise, Weierstrass was very impressed with Riemann, especially with his theory of abelian functions.

9. Cramér proved that, assuming the Riemann hypothesis, every gap is O(√p log p).

10. Other highlights include his work on abelian functions and theta functions on Riemann surfaces.

11. Tags: Apery, Apéryodial, Aperyodical, irrational numbers, Riemann zeta, Roger Apéry, series

12. There are several nontechnical books on the Riemann hypothesis, such as Derbyshire (2003), Rockmore (2005), (Sabbagh 2003a, 2003b), du Sautoy (2003).

13. His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor in Breselenz who fought in the Napoleonic Wars.

14. Integrated, say, from 1 to 3, an ordinary Riemann sum suffices to produce a result of π/6.

15. 30 We shall now briefly bring out the relationship between the Gaussian curvature and the Riemann curvature tensor.

16. It is a prototype result for many others, and is often applied in the theory of Riemann surfaces (which is its origin) and algebraic curves.

17. NAGE lindberg vermin-tenanted Communicative herniated nonbeatific thor cobwebbing Beguess obvert DISCOVERING educational Dipnoi riemann hypsometric Humanity INTERCEPTED all-constant Mining

18. In addition, from matrix versions of the Riemann equations associated with an integrable equation, multi-soliton-type solutions could be generated.

19. Some well-known examples of tensors in differential geometry are quadratic forms such as metric tensors, and the Riemann curvature tensor.

20. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis.

21. To see how the array of possibilities is again the Riemann sphere,[sentence dictionary] imagine the photon to be travelling vertically upwards.

22. Besides complex analysis (including among other subjects the Riemann–Hilbert problem), he worked on algebra and category theory and totally convex spaces.

23. The more strict analogy expressed by the 'global field' idea, in which a Riemann surface's aspect as algebraic curve is mapped to curves defined over a finite field, was built up during the 1930s, culminating in the Riemann hypothesis for curves over finite fields settled by André Weil in 1940.

24. Riemann found the correct way to extend into n dimensions the differential geometry of surfaces, which Gauss himself proved in his theorema egregium.

25. Neo-Riemannian theory is named after Hugo Riemann (1849–1919), whose "dualist" system for relating triads was adapted from earlier 19th-century harmonic theorists.

26. Heine proposed that Cantor solve an open problem that had eluded Peter Gustav Lejeune Dirichlet, Rudolf Lipschitz, Bernhard Riemann, and Heine himself: the uniqueness of the representation of a function by trigonometric series.

27. An explicit solution, in terms of Riemann invariants, is constructed from infinite-dimensional subalgebras of the symmetry algebra of the magnetohydrodynamics equations in the (1 + 2)-dimensional case.

28. Also, in the article he noted the difference between the absolute and conditional convergence of series and its impact in what was later called the Riemann series theorem.

29. Teresa Riemann bewegt sich in ihren verschiedenen Ausdrucksformen zwischen Chanson, Rock n' Roll und Atonaler neuer Musik, verknüpft sich widersprechende Formen und schafft neue Klänge

30. The Weyl Curvature tensor has the same symmetries as the Riemann Curvature tensor, but with one extra constraint: its trace (as used to define the Ricci Curvature) must vanish

31. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem).

32. To construct such varieties in the same style as for elliptic curves, starting with a lattice Λ in Cd, one must take into account the Riemann relations of abelian variety theory.

33. Elliptic geometry was developed later in the 19th century by the German mathematician Bernhard Riemann; here no parallel can be found and the angles in a triangle add up to more than 180°.

34. The known expressions for the radii of curvature of the Prandtl slipline-field are used to describe the radii of curvature in an adjoining field analytically by means of the Riemann integration method.

35. Weil was motivated by the need for a rigorous theory of correspondences on algebraic curves in positive characteristic, which he used in his proof of the Riemann hypothesis for curves over a finite field.

36. The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike (CMS Books in Mathematics) 2008th Edition by Peter Borwein (Editor), Stephen Choi (Editor), Brendan Rooney (Editor), & 3.6 out of 5 stars 8 ratings

37. In connection with the famous proof by Roger Apéry (1978) on the irrationality of the values of the Riemann zeta function evaluated at the points 2 and 3, Beukers gave a much simpler alternate proof using Legendre polynomials.

38. ‘Fermat preferred the Algebraic techniques that he used to such devastating effect in number theory.’ ‘His work in Algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.’ ‘This gave powerful results such as a purely Algebraic proof of the Riemann Roch theorem.’