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On the density of coprime m-tuples over holomorphy rings

  • Micheli, Giacomo Institute of Mathematics, University of Zurich, Winterthurerstrasse 190 8057 Zurich, Switzerland
  • Schnyder, Reto Institute of Mathematics, University of Zurich, Winterthurerstrasse 190 8057 Zurich, Switzerland
  • 2016-3-23
Published in:
  • International Journal of Number Theory. - World Scientific Pub Co Pte Lt. - 2016, vol. 12, no. 03, p. 833-839
English Let [Formula: see text] be a finite field, [Formula: see text] be a function field of genus [Formula: see text] having full constant field [Formula: see text], [Formula: see text] a set of places of [Formula: see text] and [Formula: see text] the holomorphy ring of [Formula: see text]. In this paper, we compute the density of coprime [Formula: see text]-tuples of elements of [Formula: see text]. As a side result, we obtain that whenever the complement of [Formula: see text] is finite, the computation of the density can be reduced to the computation of the [Formula: see text]-polynomial of the function field. In the genus zero case, classical results for the density of coprime [Formula: see text]-tuples of polynomials are obtained as corollaries.
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  • English
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https://sonar.rero.ch/global/documents/64365
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