Explicit bounds for primes in residue classes

@article{Bach1996ExplicitBF,
  title={Explicit bounds for primes in residue classes},
  author={Eric Bach and Jonathan P. Sorenson},
  journal={Math. Comput.},
  year={1996},
  volume={65},
  pages={1717-1735}
}
Let E/K be an abelian extension of number fields, with E 6= Q. Let ∆ and n denote the absolute discriminant and degree of E. Let σ denote an element of the Galois group of E/K. We prove the following theorems, assuming the Extended Riemann Hypothesis: (1) There is a degree-1 prime p of K such that ( p E/K ) = σ, satisfying Np ≤ (1 + o(1))(log ∆ + 2n)2. (2) There is a degree-1 prime p of K such that ( p E/K ) generates the same group as σ, satisfying Np ≤ (1 + o(1))(log ∆)2. (3) For K = Q, there… CONTINUE READING
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