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Resumen de Irreducible polynomials over finite fields produced by composition of quadratics

David Rodney Heath Brown, GIACOMO MICHELI

  • 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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