Irreducible polynomials over finite fields produced by composition of quadratics

  • David Rodney Heath-Brown

    Oxford University, UK
  • Giacomo Micheli

    Oxford University, UK
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Abstract

For a set of quadratic polynomials over a finite field, let be the (infinite) set of arbitrary compositions of elements in . In this paper we show that there are examples with arbitrarily large such that every polynomial in is irreducible. As a second result, when , we give an algorithm to determine whether all the elements in are irreducible, using only operations.

Cite this article

David Rodney Heath-Brown, Giacomo Micheli, Irreducible polynomials over finite fields produced by composition of quadratics. Rev. Mat. Iberoam. 35 (2019), no. 3, pp. 847–855

DOI 10.4171/RMI/1072