Irreducible polynomials over finite fields produced by composition of quadratics
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David Rodney Heath-Brown [1] ; Giacomo Micheli [1]
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[1] Oxford University
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 3, 2019, págs. 847-855
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
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, when #S>1, we give an algorithm to determine whether all the elements in C are irreducible, using only O(#S(logq)3q1/2) operations.
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