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The Prime Number Theorem and Generalizations

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Part of the Progress in Mathematics book series (PM, volume 157)

Abstract

It was a century ago that Jacques Hadamard and Charles de la Vallée Poussin proved (independently) the celebrated prime number theorem. If π(x) denotes the number of primes up to x, the theorem states that
$$ \mathop{{\lim }}\limits_{{x \to \infty }} \frac{{\pi \left( x \right)}}{{x/\log x}} = 1. $$

Keywords

Prime Ideal Zeta Function Simple Pole Dirichlet Series Arithmetic Progression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    W. Ellison, Prime numbers, John Wiley and Sons, Paris, Hermann, 1985.zbMATHGoogle Scholar
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    L. Féjer,Über trigonometrische Polynome, J. Reine Angew. Math., 146 (1916), pp. 53–82.Google Scholar
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    Jean-Pierre Kahane Jacques Hadamard,Math. Intelligencer, 13, 1, (1991), pp. 23–Google Scholar
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    S. Lang,Algebraic Number Theory,Springer-Verlag, 1986.Google Scholar
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    V. Kumar Murty, On the Sato-Tate conjecture, in Number Theory related to Fermat’s Last Theorem, (edN. Koblitz), Progress in Mathematics, 26, (1982), pp. 195–205.Google Scholar
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    W. Rudin, Real and Complex analysis, Bombay, Tata Mcgraw-Hill Publishing Co. Ltd., 1976.Google Scholar

Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  1. 1.Department of MathematicsQueen’s UniversityKingstonCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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