@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",

}