60
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Sieve of war: the legacy of Jitsuro Nagura

Pages 143-155 | Published online: 26 Jun 2013

References

  • Breusch , R . 1932 . Zur Verallgemeinerung des Bertrandschen Postulates, das zwischen x und 2x stets Primzahlen liegen . Mathematische Zeitschrift , : 505 – 526 . doi: 10.1007/BF01180606
  • Chebyshev , P L . 1962 . Mémoire sur les nombres premiers . Oeuvres, Chelsea ,
  • Dower , J . 1999 . Embracing defeat, Norton ,
  • Erdős , P . 1932 . Beweis eines Satzes von Tschebyschef . Acta Litterarum ac Scientiarum Szeged, Univ. Hung., Sectio mathematicarum , : 194 – 198 .
  • Gatteschi , L . 1947 . Un perfezionamento di un teorema di I. Schur sulla frequenza dei numeri primi . Bollettino Unione Mathematica Italiana , : 123 – 125 .
  • Heath-Brown , D R . 1989 . The number of primes in a short interval . Journal für die reine Angewandte Mathematik , : 162 – 193 .
  • Landau , E . 1953 . Handbuch Der Lehre von der Verteilung der Primzahlen , second edition Vol. 53 ,
  • Nagura , J . 1952 . On the interval containing at least one prime number . Proceedings of the Japan Academy , : 177 – 181 . doi: 10.3792/pja/1195570997
  • Nagura , R . 2012 . Biographical information, images, and correspondence transmitted to author ,
  • Ramanujan , S , Wilson , B M and Hardy , G H . 1927 . “ Proof of Bertrand’s postulate ” . In Collected papers , Vol. 209 , AMS Chelsea .
  • Rohrbach , H and Weis , J . 1964 . Zum finiten Fall des Bertrandschen Postulats . Journal für die reine Angewandte Mathematik , : 432 – 440 .
  • Rosser , J B . 1940 . Explicit bounds for some functions of prime numbers . American Journal of Mathematics , : 211 – 232 .
  • Schoenfeld , L . 1976 . Sharper bounds for the Chebyshev functions ϑ(x) and ψ(x) II . Mathematics of Computation , 30 : 337 – 360 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.