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Ipotèz Riemann

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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 :


Referans

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Referans istorik

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  • 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 jou

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  • 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 popilè

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Lòt referans

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

Lyen deyò

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