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Primes in Arithmetic Progression: The General Modulus

  • Harold Davenport
Part of the Graduate Texts in Mathematics book series (GTM, volume 74)

Abstract

Dirichlet’s proof of the existence of primes in a given arithmetiω progression, in the general case when the modulus q is not necessarily a prime, is in principle a natural extension of that in the special case. But the proof given in §1 that Lω(1) ≠ 0 when ω = - 1, which involved separate consideration of the cases q ≡ 1 and q 3 (mod 4), does not extend to give the analogous result that is needed when q is composite.

Keywords

Abelian Group Regular 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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Copyright information

© Ann Davenport 1980

Authors and Affiliations

  • Harold Davenport
    • 1
  1. 1.Cambridge UniversityCambridgeEngland

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