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Original Articles

Chebyshev's Bias for Products of Two Primes

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Pages 385-398 | Received 04 Aug 2009, Accepted 09 Dec 2009, Published online: 23 Feb 2011

REFERENCES

  • Chebyshev , P. L. 1853 . “Lettre de M. le professeur Tchébyshev à M. Fuss, sur un nouveau théorème rélatif aux nombres premiers contenus dans les formes 4n + 1 et 4n+3.” . Bull. de la Classe phys.-math. de l'Acad. Imp. Des Sciences St. Petersburg , 11 : 208 [Chebyshev 53]
  • Davenport , H. 2000 . Multiplicative Number Theory, , 3rd edition New York : Springer. . Graduate Texts in Mathematics 74, [Davenport 00]
  • Fiorilli , D. and Martin , G. 2009 . “Inequities in the Shanks-Rényi Prime Number Race: An Asymptotic Formula for the Densities.” arXiv:0912.4908, [Fiorilli and Martin 09]
  • Ford , K. and Konyagin , S. 2002 . “Chebyshev's Conjecture and the Prime Number Race.” . In Fourth International Conference “Modern Problems of Number Theory and Its Applications”: Current Problems, Part II (Tula, 2001) (Russian) 67 – 91 . Moscow : Mosk. Gos. Univ. im. Lomonosova, Mekh.-Mat. Fak. . [Ford and Konyagin 02]
  • Granville , A. and Martin , G. 2006 . “Prime Number Races.” . Amer. Math. Monthly , 113 ( 1 ) : 1 – 33 . [Granville and Martin 06]
  • Knapowski , S. and Turàn , P. 1962 . “Comparative Prime Number Theory I.” . Acta Math. Sci. Hungar. , 13 : 315 – 342 . [Knapowski and Turàn 62]
  • Landau , E. 1974 . Handbuch der Lehre von der Verteilung der Primzahlen, , 3rd edition New York : Chelsea. . [Landau 74]
  • Leech , J. 1957 . “Note on the Distribution of Prime Numbers.” . J. London Math. Soc. , 32 : 56 – 58 . [Leech 57]
  • Littlewood , J. E. 1914 . “Sur la distribution des nombres premiers.” . C. R. Acad. des Sciences Paris , 158 : 1869 – 1872 . [Littlewood 14]
  • Rubinstein , M. and Sarnak , P. 1994 . “Chebyshev's Bias.” . Exper. Math. , 3 : 173 – 197 . [Rubinstein and Sarnak 94]
  • Sneed , J. 2010 . “Lead Changes in the Prime Number Race.” . Math. Comp. , To appear in, [Sneed 10]

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