2008/10/02 by Winterhof, Arne, van de Woestijne, Christiaan
#11P05 #11T41 #90C10 #94B65 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.0810.0485
The Waring function g(k,q) measures the difficulty of Waring's problem for kth powers in the field of q elements. Its calculation seems to be difficult, and many partial results have been published, notably upper bounds for certain regions of the k-q-plane. In this paper, we compute the exact value of g(k,q) for two infinite families of exponent-field pairs. In these, k is large compared to q. We use a new method of proof that is mainly combinatorial in nature.