Explicit bounds for primality testing and related problems

@article{Bach1990ExplicitBF,
  title={Explicit bounds for primality testing and related problems},
  author={E. Bach},
  journal={Mathematics of Computation},
  year={1990},
  volume={55},
  pages={355-380}
}
  • E. Bach
  • Published 1990
  • Mathematics
  • Mathematics of Computation
Many number-theoretic algorithms rely on a result of Ankeny, which states that if the Extended Riemann Hypothesis (ERH) is true, any nontrivial multiplicative subgroup of the integers modulo m omits a number that is O(log2 m) . This has been generalized by Lagarias, Montgomery, and Odlyzko to give a similar bound for the least prime ideal that does not split completely in an abelian extension of number fields. This paper gives a different proof of this theorem, in which explicit constants are… Expand

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