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Pretentious multiplicative functions and the prime number theorem for arithmetic progressions

Part of: Zeta and $L$-functions: analytic theory Multiplicative number theory

Published online by Cambridge University Press:  14 May 2013

Dimitris Koukoulopoulos
Dimitris Koukoulopoulos*
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, CP 6128 succ. Centre-Ville, Montréal, QC H3C 3J7, Canada email koukoulo@dms.umontreal.ca
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Abstract

Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.

Keywords

prime number theorem for arithmetic progressionsmultiplicative functionsHalász’s theoremelementary proofs of the prime number theoremSiegel’s theorem

MSC classification

Secondary: 11M06: $zeta (s)$ and $L(s, chi)$ 11M20: Real zeros of $L(s, chi)$; results on $L(1, chi)$ 11N05: Distribution of primes 11N13: Primes in progressions

Information

Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 7 , July 2013 , pp. 1129 - 1149
Copyright
© The Author(s) 2013 

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