Rational Functions with Small Value Set
| Autor: | Herivelto Borges, Luciane Quoos, Daniele Bartoli |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Algebraic curves 010102 general mathematics Galois theory TEORIA DOS NÚMEROS Value (computer science) Rational function Rational functions 01 natural sciences Combinatorics Algebraic curves Finite fields Galois theory Rational functions Value sets Finite field Field extension 0103 physical sciences Value sets Finite fields 010307 mathematical physics Algebraic curve 0101 mathematics Connection (algebraic framework) Prime power Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| DOI: | 10.14760/owp-2020-05 |
| Popis: | 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. Oberwolfach Preprints;2020,05 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|