Exact solutions to Waring's problem for finite fields
Abstract
The Waring function $g(k,q)$ measures the difficulty of Waring's problem for $k$th 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 exponentfield pairs. In these, $k$ is large compared to $q$. We use a new method of proof that is mainly combinatorial in nature.
 Publication:

arXiv eprints
 Pub Date:
 October 2008
 arXiv:
 arXiv:0810.0485
 Bibcode:
 2008arXiv0810.0485W
 Keywords:

 Mathematics  Number Theory;
 11P05;
 11T41;
 90C10;
 94B65
 EPrint:
 21 pages