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The prime number theorem via the large sieve

Published online by Cambridge University Press:  26 February 2010

Adolf Hildebrand
Adolf Hildebrand
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A.
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Extract

In the last three decades there appeared a number of elementary proofs of the prime number theorem (PNT) in the literature (see [3] for a survey). Most of these proofs are based, at least in part, on ideas from the original proof by Erdős [5] and Selberg [12]. In particular, one of the main ingredients of the Erdős-Selberg proof, Selberg's formula

(where p and q run through primes) appears, in some form, in almost all these proofs.

Type
Research Article
Information
Mathematika , Volume 33 , Issue 1 , June 1986 , pp. 23 - 30
Copyright
Copyright © University College London 1986

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References

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