On the Waring problem with multivariate Dickson polynomials

Alina Ostafe*, David Thomson, Arne Winterhof

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

Abstract

We extend recent results of Gomez and Winterhof, and Ostafe and Shparlinski on the Waring problem with univariate Dickson polynomials in a finite field to the multivariate case. We give some sufficient conditions for the existence of the Waring number for multivariate Dickson polynomials, that is, the smallest number g of summands needed to express any element of the finite field as sum of g values of the Dickson polynomial. Moreover, we prove strong bounds on the Waring number using a reduction to the case of fewer variables and an approach based on recent advances in arithmetic combinatorics due to Glibichuk and Rudnev.

Original languageEnglish
Title of host publicationTheory and applications of finite fields
EditorsMichel Lavrauw, Gary L. Mullen, Svetla Nikova, Daniel Panario, Leo Storme
Place of PublicationProvidence, RI
PublisherAmerican Mathematical Society
Pages153-161
Number of pages9
ISBN (Print)9780821852989
DOIs
Publication statusPublished - 2012
Event10th International Conference on Finite Fields and Their Applications - Ghent, Belgium
Duration: 11 Jul 201115 Jul 2011

Publication series

NameContemporary Mathematics
PublisherAMER MATHEMATICAL SOC
Volume579
ISSN (Print)0271-4132

Conference

Conference10th International Conference on Finite Fields and Their Applications
CountryBelgium
CityGhent
Period11/07/1115/07/11

Keywords

  • FINITE-FIELDS

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