2021/08/18 by Martha Rzedowski–Calderón, Gabriel Villa–Salvador, Rzedowski-Calderón, Martha +1
Mathematics · #11R58 (Primary) 11R29 #11R60 (Secondary) #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.2108.08337
openalex publication_date 2021/08/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We obtain the extended genus field of an abelian extension of a rational\nfunction field. We follow the definition of Angl `es and Jaulent, which uses\nclass field theory. First we show that the natural definition of extended genus\nfield of a cyclotomic function field obtained by means of Dirichlet characters\nis the same as the one given by Angl `es and Jaulent. Next we study the\nextended genus field of a finite abelian extension of a rational function field\nalong the lines of the study of genus fields of abelian extensions of rational\nfunction fields and compare this approach with the one given by Angl `es and\nJaulent.\n