Irreducible polynomials over finite fields produced by composition of quadratics

• David Rodney Heath-Brown ^[1] ; Giacomo Micheli ^[1]
  1. [1] Oxford University
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 3, 2019, págs. 847-855
• Idioma: inglés
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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.