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- W4382317275 abstract "Rational transformations of polynomials are extensively studied in the context of finite fields, especially for the construction of irreducible polynomials. In this paper, we consider the factorization of rational transformations with (normalized) generators of the field $K(x)^G$ of $G$-invariant rational functions for $G$ a finite subgroup of $operatorname{PGL}_2(K)$, where $K$ is an arbitrary field. Our main theorem shows that the factorization is related to a well-known group action of $G$ on a subset of monic polynomials. With this, we are able to extend a result by Lucas Reis for $G$-invariant irreducible polynomials. Additionally, some new results about the number of irreducible factors of rational transformations for $Q$ a generator of $mathbb{F}_q(x)^G$ are given when $G$ is non-cyclic." @default.
- W4382317275 created "2023-06-28" @default.
- W4382317275 creator A5054522572 @default.
- W4382317275 date "2023-06-23" @default.
- W4382317275 modified "2023-09-27" @default.
- W4382317275 title "Rational Transformations and Invariant Polynomials" @default.
- W4382317275 doi "https://doi.org/10.48550/arxiv.2306.13502" @default.
- W4382317275 hasPublicationYear "2023" @default.
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