Irreducible polynomials with prescribed trace and restricted norm

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

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.
25 pages

Keywords

Number Theory, 12E05

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/140036

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.2767
 http://arxiv.org/abs/0710.2767

Collections

arXiv