Primes in Arithmetic Progression: The General Modulus

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


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.


Abelian Group Regular Function Simple Pole Dirichlet Series Arithmetic Progression 
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Copyright information

© Ann Davenport 1980

Authors and Affiliations

  • Harold Davenport
    • 1
  1. 1.Cambridge UniversityCambridgeEngland

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