On the computation of integral closures of cyclic extensions of function fields

Abstract: Let S be a non-empty proper subset of the set of places of a global function field F, and E a cyclic Kummer or Artin–Schreier–Witt extension of F. The author presents a method of efficiently computing the ring of elements of E which are integral at all places of S. As an important tool, he includes an algorithmic version of the strong approximation theorem. The paper concludes with several examples.