Irreducible polynomials over finite fields produced by composition of quadratics

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 algori...

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Bibliographic Details
Main Authors: Heath-Brown, DR, Micheli, G
Format: Journal article
Language:English
Published: European Mathematical Society 2019