On the Waring problem with Dickson polynomials modulo a prime

We improve recent results of D. Gomez and A. Winterhof (2010) and of A. Ostafe and I. E. Shparlinski (2011) on the Waring problem with Dickson polynomials in the case of prime finite fields. Our approach is based on recent bounds of Kloosterman and Gauss sums due to A. Ostafe, I. E. Shparlinski and J. F. Voloch (2021).