On primitive roots of one-dimensional tori

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Abstract

We exploit an analogue of Artin's primitive roots conjecture for one-dimensional tori over ℚ. Let T be a one-dimensional torus over ℚ, and let P ε T(ℚ) be a nontorsion point. Under Generalized Riemann Hypothesis, we derive an explicit density formula for the set of rational primes ℓ such that P modulo ℓ generates T(F).

Original languageEnglish
Pages (from-to)23-33
Number of pages11
JournalJournal of Number Theory
Volume93
Issue number1
DOIs
StatePublished - 2002

Keywords

  • Density
  • Primitive roots
  • Quadratic fields
  • Torus

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