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A note on extended genus fields of Kummer extensions of rational function fields

2024/03/01 by Martha Rzedowski–Calderón, Gabriel Villa–Salvador, Rzedowski-Calderón, Martha +1
Mathematics · #11R29 #11R58 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2403.01021

openalex publication_date 2024/03/01 · openalex created_date 2024/03/06 · openalex updated_date 2026/07/28

Abstract

We consider the generalization of the extended genus field of a prime degree cyclic Kummer extension of a rational function field obtained by R. Clement in 1992 to general Kummer extensions. We observe that the same approach of Clement works in general.

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