Browsing by Author "Borges, Herivelto"

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    Rational Functions with Small Value Set
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2020) Bartoli, Daniele; Borges, Herivelto; Quoos, Luciane
    In connection with Galois Theory and Algebraic Curves, this paper investigates rational functions h(x)=f(x)/g(x)∈Fq(x) for which the value set Vh={h(α)|α∈Fq∪{∞}} is relatively small. In particular, under certain circumstances, it proves that h(x) having a small value set is equivalent to the field extension Fq(x)/Fq(h(x)) being Galois.