Irreducible polynomials over finite fields produced by composition of quadratics
| Autor: | Giacomo Micheli, D. R. Heath-Brown |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Polynomial
Pure mathematics Mathematics - Number Theory Dynamical systems theory General Mathematics 010102 general mathematics Composition (combinatorics) 01 natural sciences Set (abstract data type) Arbitrarily large Finite field Quadratic equation FOS: Mathematics Number Theory (math.NT) 0101 mathematics Mathematics |
| Zdroj: | Revista Matemática Iberoamericana. 35:847-855 |
| ISSN: | 0213-2230 |
| DOI: | 10.4171/rmi/1072 |
| Popis: | For a set $S$ of quadratic polynomials over a finite field, let $C$ be the (infinite) set of arbitrary compositions of elements in $S$. In this paper we show that there are examples with arbitrarily large $S$ such that every polynomial in $C$ is irreducible. As a second result, we give an algorithm to determine whether all the elements in $C$ are irreducible, using only $O( \#S (\log q)^3 q^{1/2} )$ operations. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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