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Primes in Arithmetic Progression
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applies argument arithmetic progressions assume bound character mod coefficients combination complex consider constant containing continuous contribution converges corresponding deduced defined definition denote depending Dirichlet's discriminant earlier easily equivalent estimate exists expression fact factor finite fixed follows formula functional equation further given gives Hence holds identity implies imprimitive inequality integral large sieve later limit Math means method mod q modulus q multiplicative O(log obtain particular periods pole positive positive constant possible prime prime number theorem principal proof proved quadratic range real primitive character regular relation relatively remains replaced representation residue result Riemann root satisfies side simple suffices summation suppose symbol theory trivial valid zeros Σ Σ