Exact solutions to Waring's problem for finite fields
| dc.creator | Winterhof, Arne | |
| dc.creator | van de Woestijne, Christiaan | |
| dc.date | 2008-10-02 | |
| dc.date.accessioned | 2026-07-07T10:07:09Z | |
| dc.date.available | 2026-07-07T10:07:09Z | |
| dc.description | 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. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/0810.0485 | |
| dc.identifier | http://arxiv.org/abs/0810.0485 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170536 | |
| dc.subject | Number Theory | |
| dc.subject | 11P05; 11T41, 90C10, 94B65 | |
| dc.title | Exact solutions to Waring's problem for finite fields | |
| dc.type | text |