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Original Articles

Chebyshev's Bias

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Pages 173-197 | Published online: 03 Apr 2012

REFERENCES

  • Armitage , J. V. 1972 . ”Zeta functions with a zero at s = ¼“ . Inv. Math. , 15 : 199 – 205 . [Armitage 1972]
  • Bays , C. and Hudson , R. H. 1978 . ”Details of the first region of integers x with π3,2x) < πT3,1x)“ . Math. Comp. , 32 : 571 – 760 . [Bays and Hudson 1978]
  • Char , B. W. 1991 . Maple V Language Reference Manual and Maple V Library Reference Manual New York : Springer. . [Char et al. 1991]
  • Davenport , H. 1980 . Multiplicative Number Theory, , 2nd. ed Berlin : Springer. . [Davenport 1980], Graduate Texts in Mathematics 74
  • Davidoff , G. 1994 . “Some experimental results on a generalization of Littlewood's Theorem” Mount Holyoke College. . [Davidoff 1994], preprint
  • Dirichlet , L. 1837 . ”Beweis des Satzes, daß jede unbegrenzte arithmetische Progression. unendlich viele Primzahlen enthält“ . Abh. König. Preuss. Akad. , 34 : 45 – 81 . [Dirichlet 1837], Reprinted on pp. 313–342 in Dirichlets Werke, vol. 1, Reimer, Berlin, 1889–97 and Chelsea, Bronx (NY), 1969
  • Heath-Brown , R. 1992 . ”The distribution and moments of the error term in the Dirichlet divisor problem“ . Acta Arith. , 60 ( 4 ) : 389 – 415 . [Heath-Brown 1992]
  • Hooley , C. 1977 . ”On the Barban–Davenport–Halberstam Theorem: VII“ . J. London Math. Soc. (2) , 16 : 1 – 8 . [Hooley 1977]
  • Ingham , A. E. 1932 . The Distribution of Prime Numbers Cambridge : Cambridge University Press. . [Ingham 1932]
  • Kaczorowski , J. “The boundary values of generalized Dirichlet series and a problem of Chebyshev” Poznań University. . [Kaczorowski], preprint
  • Knapowsky , S. and Turan , P. 1962 . ”Comparative prime number theory I“ . Acta. Math. Acad. Sci. Hungar. , 13 : 299 – 314 . [Knapowsky and Turan 1962], Reprinted on pp. 1329–1343 in Collected papers of Paul Turan, vol. 2 (Erd, P. ös), Akadémiai Kiadó, Budapest, 1990
  • Kueh , K. L. 1988 . ”The moments of infinite series“ . J. reine angew. Math. , 385 : 1 – 9 . [Kueh 1988]
  • Lang , S. 1970 . Algebraic Number Theory Reading , MA : Addison-Wesley. . [Lang 1970]
  • Leech , J. 1957 . ”Note on the distribution of prime numbers“ . J. London Math. Soc. , 32 : 56 – 58 . [Leech 1957]
  • Lévy , P. 1922 . ”Sur la détermination des lois de probabilityé par leurs functions caractéristiques“ . C. R. Acad. Sci. Paris , 175 : 854 – 856 . [Lévy 1922]
  • Littlewood , J. E. 1914 . ”Distribution des Nombres Premiers“ . C. R. Acad. Sci. Paris , 158 : 1869 – 1872 . [Littlewood 1914]
  • Littlewood , J. E. 1928 . ”On the Class-Number of the Corpus P(√–k)“ . Proc. London Math. Soc. (2) , 27 : 358 – 372 . [Littlewood 1928]
  • Montgomery , H. L. “The Zeta Function and Prime Numbers” . Proceedings of the Queen's Number Theory Conference . 1979 . Edited by: Ribenboim , P. pp. 14 – 24 . Kinston , Ont. : Queen's University. . [Montgomery 1980]
  • Odlyzko , A. “The 1020-th zero of the Riemann Zeta Function and 70 million of its neighbours” [Odlyzko], preprint
  • Phillips , R. and Sarnak , P. 1987 . ”Geodesies in homology classes“ . Duke Math. J. , 55 : 287 – 297 . [Phillips and Sarnak 1987]
  • te Riele , H. J. J. 1986 . ”On the sign change of the difference π(x) – Li(x)“ . Math. Comp. , 48 : 667 – 81 . [te Riele 1986]
  • Rubinstein , M. 1994 . “Chebyshev's bias” Princeton University. . [Rubinstein 1994], senior thesis
  • Rudnick , Z. and Sarnak , P. 1994 . “Zeros of principal L-functions and random matrix theory” Princeton University. . [Rudnick and Sarnak 1994], preprint
  • Rumely , R. 1993 . ”Numerical computations concerning ERH“ . Math Comp. , 61 : 415 – 440 . [Rumely 1993]
  • Serre , J.-P. 1971 . “Conducteurs d'Artin des charactères réels . Inv. Math. , 14 : 173 – 183 . [Serre 1971]
  • Shanks , D. 1959 . ”Quadratic residues and the distribution of primes“ . Math. Tables (later Math. Comp.) , 13 : 272 – 284 . [Shanks 1959]
  • Skewes , S. 1933 . ”On the difference π(x) – Li(x)“ . J. London Math. Soc. , 8 : 277 – 83 . [Skewes 1933]
  • Stein , E. and Weiss , G. 1971 . Introduction to Fourier Analysis on Euclidean Spaces Princeton : Princeton University Press. . [Stein and Weiss 1971]
  • Watson , G. N. 1948 . A Treatise on the Theory of Bessel Functions, , 2nd ed. Cambridge : Cambridge University Press. . [Watson 1948]
  • Wintner , A. 1938 . “Asymptotic Distributions and Infinite Convolutions” Princeton : Notes distributed by the Institute for Advanced Study. . [Wintner 1938]
  • Wintner , A. 1941 . ”On the distribution function of the remainder term of the prime number theorem“ . Amer. J. Math. , 63 : 233 – 48 . [Wintner 1941]

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