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Abstract Let q be a prime power, and let F q be the finite field with q elements. In connection with Galois theory and algebraic curves, this paper investigates rational… Click to show full abstract
Abstract Let q be a prime power, and let F q be the finite field with q elements. In connection with Galois theory and algebraic curves, this paper investigates rational functions h ( x ) = f ( x ) / g ( x ) ∈ F q ( x ) for which the value sets V h = { h ( α ) | α ∈ F q ∪ { ∞ } } are relatively small. In particular, under certain circumstances, it proves that h ( x ) having a small value set is equivalent to the field extension F q ( x ) / F q ( h ( x ) ) being Galois.
Keywords:
value set;
value;
rational functions;
functions small;
small value
Journal Title: Journal of Algebra
Year Published: 2020
Link to full text (if available)
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Journal Title: Journal of Algebra
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!