• Corpus ID: 116271642

On Artin's Conjecture for Primitive Roots

  title={On Artin's Conjecture for Primitive Roots},
  author={Francesco Pappalardi},
Various generalizations of the Artin’s Conjecture for primitive roots are considered. It is proven that for at least half of the primes p, the first log p primes generate a primitive root. A uniform version of the Chebotarev Density Theorem for the field Q(ζl, 2 ) valid for the range l < log x is proven. A uniform asymptotic formula for the number of primes up to x for which there exists a primitive root less than s is established. Lower bounds for the exponent of the class group of imaginary… 
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