Irreducible polynomials with prescribed trace and restricted norm
| dc.creator | Kononen, K. | |
| dc.creator | Moisio, M. | |
| dc.creator | Rinta-aho, M. | |
| dc.creator | Vaananen, K. | |
| dc.date | 2007-10-15 | |
| dc.date.accessioned | 2026-07-07T08:36:22Z | |
| dc.date.available | 2026-07-07T08:36:22Z | |
| dc.description | Let GF(q), q=p^r, be a finite field with a primitive element g. In this paper we use exponential sums and Jacobi sums to compute the number of the irreducible polynomials of degree m over GF(q) with trace fixed and norm restricted to a coset of a subgroup <g^s>, s|(q-1). We give the number explicitly for s=2, 3, 4 when q=p, and for s|(p^e+1) when r=2en. Finally, we give explicit formulae for the number when both trace and norm are fixed, p=2 and m =< 30. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/0710.2767 | |
| dc.identifier | http://arxiv.org/abs/0710.2767 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140036 | |
| dc.subject | Number Theory | |
| dc.subject | 12E05 | |
| dc.title | Irreducible polynomials with prescribed trace and restricted norm | |
| dc.type | text |