Exact solutions to Waring's problem for finite fields

@article{Winterhof2008ExactST,
  title={Exact solutions to Waring's problem for finite fields},
  author={Arne Winterhof and Christiaan E. van de Woestijne},
  journal={Acta Arithmetica},
  year={2008},
  volume={141},
  pages={171-190}
}
with xi ∈ Fq, i.e., as a sum of kth powers of elements of Fq. We can then define the Waring function g(k, q) as the maximal number of summands needed to express all elements of Fq as sums of kth powers. We note that, by an easy argument, we have g(k, q) = g(k, q), where k = gcd(k, q − 1). Hence, we will assume from now on that k divides q − 1. Several authors have established bounds on the value of g(k, q) for various choices of the parameters k and q – a survey is given in [8]. For the cases… Expand
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