The Prime Distribution

Part of the Springer Series in Information Sciences book series (SSINF, volume 7)


Numerical Evidence Riemann Hypothesis Probability Factor Spacing Pattern Asymptotic Density 


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Chapter 4

  1. 4.1
    P. Erdös, M. Kac: The Gaussian law of errors in the theory of additive number theoretic functions. Am. J. Math. 62, 738–742 (1945)CrossRefGoogle Scholar
  2. 4.2
    P. D. T. A. Elliot: Probabilistic Number Theory, Vols. 1–2 (Springer, Berlin, Heidelberg, New York 1980)Google Scholar
  3. 4.3
    D. Zagier: “Die ersten 50 Millionen Primzahlen” in Lebendige Zahlen, ed. by F. Hirzebruch (Birkhäuser, Basel 1981)Google Scholar
  4. 4.4
    G. Kolata: Does Gödel’s theorem matter to mathematics? Science 218, 779–780 (1982)MathSciNetADSCrossRefGoogle Scholar
  5. 4.5
    P. Erdös: On a new method in elementary number theory which leads to an elementary proof of the prime number theorem. Proc. Nat. Acad. Sci. U.S.A. 35, 374–384 (1949)MathSciNetMATHADSCrossRefGoogle Scholar
  6. 4.6
    H. M. Edwards: Riemann’s Zeta Function (Academic Press, New York 1974)MATHGoogle Scholar
  7. 4.7
    Z. Füredi, J. Komlos: The eigenvalues of random symmetric matrices. Combinatorica 1, 233–241 (1981)MathSciNetMATHCrossRefGoogle Scholar
  8. 4.8
    M. R. Schroeder: A simple function and its Fourier transform. Math. Intelligencer 4, 158–161 (1982)MathSciNetCrossRefGoogle Scholar
  9. 4.9
    U. Dudley: Elementary Number Theory (Freeman, San Francisco 1969)MATHGoogle Scholar
  10. 4.10
    G. H. Hardy, E. M. Wright: An Introduction to the Theory of Numbers, 5th ed. Sect. 22.3 (Clarendon, Oxford 1984)Google Scholar
  11. 4.11
    M. R. Schroeder: Speech Communication 1, 9 (1982)CrossRefADSGoogle Scholar
  12. 4.12
    I. M. Vinogradov: An Introduction to the Theory of Numbers (Pergamon, New York 1955)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2006

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