Liu, Yu-RuWooley, Trevor D.2023-10-032023-10-032007-09https://doi.org/10.7169/facm/1229619654http://hdl.handle.net/10012/19986Copyright © 2007 Adam Mickiewicz UniversityLet J k q [t] denote the additive closure of the set of k th powers in the polynomial ring Fq[t], defined over the finite field Fq having q elements. We show that when s>k + 1 and q>k 2k+2 , then every polynomial in J k q [t] is the sum of at most s k th powers of polynomials from Fq[t]. When k is large and s>( 4 3 + o(1))k log k , the same conclusion holds without restriction on q . Refinements are offered that depend on the characteristic of Fq .enfunction fieldsWaring's ProblemArticle