On the Waring Problem with multivariate Dickson polynomials
Alina Ostafe, David Thomson, Arne Winterhof · Contemporary mathematics - American Mathematical Society · 2012
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 g of summands needed to express any element of the finite field as sum of g 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.