Arne Winterhof, Christiaan van de Woestijne
Published 2008-10-02Version 1
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 exponent-field pairs. In these, $k$ is large compared to $q$. We use a new method of proof that is mainly combinatorial in nature.
Graphs associated with the map $x \mapsto x+x^{-1}$ in finite fields of characteristic two
On Taking Square Roots without Quadratic Nonresidues over Finite Fields
On the group orders of elliptic curves over finite fields
![QR code for arXiv:0810.0485 [math.NT]](http://oss.arxitics.com/images/favicon.svg)