The Prime Number Theorem and Generalizations

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


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
$$ \mathop{{\lim }}\limits_{{x \to \infty }} \frac{{\pi \left( x \right)}}{{x/\log x}} = 1. $$


Prime Ideal Zeta Function Simple Pole Dirichlet Series Arithmetic Progression 
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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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