Primes in Arithmetic Progression: The General Modulus
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.
KeywordsAbelian Group Regular Function Simple Pole Dirichlet Series Arithmetic Progression
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