Translator Disclaimer
September 2007 The unrestricted variant of Waring's problem in function fields
Yu-Ru Liu, Trevor D. Wooley
Funct. Approx. Comment. Math. 37(2): 285-291 (September 2007). DOI: 10.7169/facm/1229619654

Abstract

Let $\mathbb{J}_q^k[t]$ denote the additive closure of the set of $k$th powers in the polynomial ring $\mathbb{F}_q[t]$, defined over the finite field $\mathbb{F}_q$ having $q$ elements. We show that when $s\ge k+1$ and $q \ge k^{2k+2}$, then every polynomial in $\mathbb{J}_q^k[t]$ is the sum of at most $s$ $k$th powers of polynomials from $\mathbb{F}_q[t]$. When $k$ is large and $s \ge (\frac{4}{3}+o(1)) k\log k$, the same conclusion holds without restriction on $q$. Refinements are offered that depend on the characteristic of $\mathbb{F}_q$.

Citation

Download Citation

Yu-Ru Liu. Trevor D. Wooley. "The unrestricted variant of Waring's problem in function fields." Funct. Approx. Comment. Math. 37 (2) 285 - 291, September 2007. https://doi.org/10.7169/facm/1229619654

Information

Published: September 2007
First available in Project Euclid: 18 December 2008

zbMATH: 1226.11105
MathSciNet: MR2363827
Digital Object Identifier: 10.7169/facm/1229619654

Subjects:
Primary: 11P05
Secondary: 11P55, 11T55

Rights: Copyright © 2007 Adam Mickiewicz University

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.37 • No. 2 • September 2007
Back to Top