Invariant theory of a special group action on irreducible polynomials over finite fields

2017/08/23 by Reis, Lucas
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.06862

Abstract

In the past few years, an action of PGL₂(\mathbb F_q) on the set of irreducible polynomials in \mathbb F_q[x] has been introduced and many questions have been discussed, such as the characterization and number of invariant elements. In this paper, we analyze some recent works on this action and provide full generalizations of them, yielding final theoretical results on the characterization and number of invariant elements.

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• A group action on multivariate polynomials over finite fields
• On the existence and number of invariant polynomials
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• Rational Transformations and Invariant Polynomials