Reciprocity by resultant in

  • Pete L. Clark

    University of Georgia, Athens, USA
  • Paul Pollack

    University of Georgia, Athens, USA
Reciprocity by resultant in $k[t]$ cover
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Abstract

Let be a perfect field with procyclic absolute Galois group and containing a primitive -th root of unity. We define a degree power residue symbol in the ring , show that it is equal to “the character of the resultant Res” and deduce a reciprocity law. We are motivated by commonalities between the classical case and the novel but very simple case .

Cite this article

Pete L. Clark, Paul Pollack, Reciprocity by resultant in . Enseign. Math. 65 (2019), no. 1/2, pp. 101–116

DOI 10.4171/LEM/65-1/2-3