Rational Functions with Small Value Set

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Date
2020-03-14MFO Scientific Program
Research in Pairs 2019Series
Oberwolfach Preprints;2020,05Author
Bartoli, Daniele
Borges, Herivelto
Quoos, Luciane
Metadata
Show full item recordOWP-2020-05
Abstract
In connection with Galois Theory and Algebraic Curves, this paper investigates rational
functions $h(x) = f(x)/g(x) \in \mathbb{F}_q(x)$ for which the value set $V_h = {\{h(α) | α \in \mathbb{F}_q \cup\{\infty\}}\}$ is relatively small. In particular, under certain circumstances, it proves that $h(x)$ having a small value set is equivalent to the field extension $\mathbb{F}_q(x)/\mathbb{F}_q(h(x))$ being Galois.