Ipotèz Riemann

konjekti sou fonksyon zêta Reimann nan, ki lye ak repatisyon nonb premye yo

Se yon ipotèz matematik, yon konjekti fèt pa Bernhard Riemann.

pati reyèl an wouj, pati imajinè an ble de fonksyon Zeta Riemann anlè liy kritik Re(s) = 1/2

Kesyon l poze ap prezante konsa : èske tout zero fonksyon Zeta Riemann an genyen 1/2 pou pati reyèl ?

Li twouve yon fomilasyon pli senp pa :


Pou tout ε > 0, nou genyen

lè π(x) ap deziyen kantite nonm premye ki anvan x, ln(x) se fonksyon logaritm, evalye nan x, epi a dwat ou ap twouve notasyon Landau.

Yon vèsyon ki pa asenptotik pa Lowell Schoenfeld, ap di ke ipotèz Riemann an ekivalan a :


ReferansChanje

Referans istorikChanje

  • Bernhard Riemann, Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse, (1859) Monatsberichte der Berliner Akademie. (This site provides both a facsimile of the original manuscripts, as well as English translations.)
  • Jacques Hadamard, Sur la distribution des zéros de la fonction ζ(s) et ses conséquences arithmétiques, Bulletin Société Mathématique de France 14 (1896) pp 199-220.

Teknik jodi jouChanje

  • H. M. Edwards, Riemann's Zeta Function, Academic Press, 1974. (Reprinted by Dover Publications, 2001 ISBN 0-486-41740-9)
  • E. C. Titchmarsh, The Theory of the Riemann Zeta Function, second revised (Heath-Brown) edition, Oxford University Press, 1986
  • Jeffrey Lagarias (2002). « An Elementary Problem Equivalent to the Riemann Hypothesis ». American Mathematical Monthly 109: 534–543.  (A relationship in terms of Harmonic numbers.)
  • (no author credited), Computation of zeros of the Zeta function (2004). (Reviews the GUE hypothesis, provides an extensive bibliography as well).
  • Schoenfeld, Lowell. "Sharper bounds for the Chebyshev functions θ(x) and ψ(x). II." Mathematics of Computation 30 (1976), no. 134, 337--360.
  • Conrey, J. Brian. "the Riemann Hypothesis" Notices of the American Mathematical Society, March 2003, 341-353. Available free http://www.ams.org/notices/200303/fea-conrey-web.pdf

Referans popilèChanje

Lòt referansChanje

  • Bollobas, Bela, foreword to Littlewood's Miscellany, Cambridge University Press, 1986

Lyen deyòChanje