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arXiv · 1903.10846

Number of irreducible polynomials whose compositions with monic monomials have large irreducible factors

Sabina B. Pannek
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Abstract

Given a prime power $q$ and positive integers $m,t,e$ with $e > mt/2$, we determine the number of all monic irreducible polynomials $f(x)$ of degree $m$ with coefficients in $\mathbb{F}_q$ such that $f(x^t)$ contains an irreducible factor of degree $e$. Polynomials with these properties are important for justifying randomised algorithms for computing with matrix groups.

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Sabina B. Pannek. 2019-03-26. Number of irreducible polynomials whose compositions with monic monomials have large irreducible factors. https://arxiv.org/abs/1903.10846

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