2013/01/11 by Guillaume Rond, Rond, Guillaume
Mathematics · #14B12 #Commutative Algebra (math.AC) #FOS: Mathematics #Meromorphic and Entire Functions #Primary 13B40 #Secondary 13P99 #math.AC #msc:13B40 #msc:13P99 #msc:14B12
paper · pdf · doi:10.48550/arxiv.1301.2418
Published in Journal of Algebra
arxiv created 2013/01/11 · openalex publication_date 2013/01/11 · arxiv updated 2013/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to give an effective version of the Strong Artin Approximation Theorem for binomial equations. First we give an effective version of the Greenberg Approximation Theorem for polynomial equations, then using the Weierstrass Preparation Theorem, we apply this effective result to binomial equations. We prove that the Artin function of a system of binomial equations is bounded by a doubly exponential function in general and that it is bounded by an affine function if the order of the approximated solutions is bounded.