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Analytic Proof of the Prime Number Theorem

  • Tom M. Apostol
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

The prime number theorem is equivalent to the statement
$$\psi (x) \sim xasx \to \infty$$
(1)
whereΨ(x) is Chebyshev’s function,
$$\psi (x) = \sum\limits_{n \leqslant x} { \wedge (n)}$$
.

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Copyright information

© Springer Science+Business Media New York 1976

Authors and Affiliations

  • Tom M. Apostol
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

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