Some arithmetical functions in finite fields
Glasgow mathematical journal, Tome 11 (1970) no. 1, pp. 21-36
Voir la notice de l'article provenant de la source Cambridge University Press
In this paper, we investigate various “arithmetical” functions associated with the factorisation of polynomials in GF[q, X1, ..., Xk], where k ≥ 1 and GF[q]is the finite field of order q. We shall assume throughout that all polynomials discussed are non-zero and have been normalised by selecting one polynomial from each equivalence class with respect to multiplication by non-zero elements of GF[q]. The constant polynomial will be denoted by 1. With this normalisation, GF[q, X1, ..., Xk] becomes a unique factorisation domain. When k = 1, normalisation is achieved by considering only monic polynomials. By the degree of a polynomial A(X1, ..., Xk) will be understood the ordered set (m1, ..., mk), where m1 is the degree of A(X1, ..., Xk) in X1,(i = 1, ..., k).
Cohen, Stephen D. Some arithmetical functions in finite fields. Glasgow mathematical journal, Tome 11 (1970) no. 1, pp. 21-36. doi: 10.1017/S001708950000080X
@article{10_1017_S001708950000080X,
author = {Cohen, Stephen D.},
title = {Some arithmetical functions in finite fields},
journal = {Glasgow mathematical journal},
pages = {21--36},
year = {1970},
volume = {11},
number = {1},
doi = {10.1017/S001708950000080X},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950000080X/}
}
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