On Artin's conjecture and Euclid's algorithm in global fields

@article{Lenstra1977OnAC,
  title={On Artin's conjecture and Euclid's algorithm in global fields},
  author={H. Lenstra},
  journal={Inventiones mathematicae},
  year={1977},
  volume={42},
  pages={201-224}
}
  • H. Lenstra
  • Published 1977
  • Mathematics
  • Inventiones mathematicae
This paper considers a generalization of Artin's conjecture on primes with prescribed primitive roots. The main result provides & necessary and sufficient condition for the conjectural density of certain sets of primes to be non-zero. As an application a theorem about the existence of a euclidean algorithm in rings of arithtnetic type is proved. Key_word£: Artin's conjecture, primitive roots, Euclid's algorithm. 12A75, 10HI5, 12A45, 13F10. On Artin's conjecture and Euclid's algorithm in global… Expand
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