@inproceedings{3b4e5caf478645e79f09ed1cb82bc12d,
title = "On the Waring problem with multivariate Dickson polynomials",
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.",
keywords = "FINITE-FIELDS",
author = "Alina Ostafe and David Thomson and Arne Winterhof",
year = "2012",
doi = "10.1090/conm/579/11527",
language = "English",
isbn = "9780821852989",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "153--161",
editor = "Michel Lavrauw and Mullen, {Gary L.} and Svetla Nikova and Daniel Panario and Leo Storme",
booktitle = "Theory and applications of finite fields",
address = "United States",
note = "10th International Conference on Finite Fields and Their Applications ; Conference date: 11-07-2011 Through 15-07-2011",
}