Representation of powers by polynomials over function fields and a problem of Logic

2011/07/20 by Hector Pasten, Héctor Pastén, Pasten, Hector
Computer Science · Mathematics · #11R58 #11U05 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.NT #msc:11R58 #msc:11U05

paper · pdf · doi:10.48550/arxiv.1107.4019

arxiv created 2011/07/20 · openalex publication_date 2011/07/20 · arxiv updated 2011/07/21 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

Abstract

We solve a generalization of Büchi's problem in any exponent for function fields, and briefly discuss some consequences on undecidability. This provides the first example where this problem is solved for rings of functions in the case of an exponent larger than 3.

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