Prescribing coefficients of invariant irreducible polynomials
Kapetanakis, Georgios (2017) Prescribing coefficients of invariant irreducible polynomials. (Accepted/In Press)
Official URL: http://dx.doi.org/10.1016/j.jnt.2017.05.003
Let Fq be the finite field of q elements. We define an action of PGL(2,q) on Fq[X] and study the distribution of the irreducible polynomials that remain invariant under this action for lower-triangular matrices. As a result, we describe the possible values of the coefficients of such polynomials and prove that, with a small finite number of possible exceptions, there exist polynomials of given degree with prescribed high-degree coefficients.
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