Dickson curves
Let kq denote the finite field of order q and odd characteristic p. For a∈kq, let gd(x,a) denote the Dickson polynomial of degree d defined by gd(x,a)=∑i=0[d/2]d/(d−i)(d−ii)(−a)ixd−2i. Let f(x) denote a monic polynomial with coefficients in kq. Assume that f2(x)−4 is not a perfect square and...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/42818 |
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| _version_ | 1832545734279299072 |
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| author | Javier Gomez-Calderon |
| author_facet | Javier Gomez-Calderon |
| author_sort | Javier Gomez-Calderon |
| collection | DOAJ |
| description | Let kq
denote the finite field of order q
and odd
characteristic p. For a∈kq, let gd(x,a)
denote the
Dickson polynomial of degree d
defined by gd(x,a)=∑i=0[d/2]d/(d−i)(d−ii)(−a)ixd−2i. Let f(x)
denote a monic
polynomial with coefficients in kq. Assume that f2(x)−4
is not a perfect square and gcd(p,d)=1. Also assume that
f(x)
and g2(f(x),1)
are not of the form gd(h(x),c). In this note, we show that the polynomial gd(y,1)−f(x)∈kq[x,y]
is absolutely irreducible. |
| format | Article |
| id | doaj-art-b86d8fb3bdad45bf90aa470c6f86d7ab |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b86d8fb3bdad45bf90aa470c6f86d7ab2025-02-03T07:24:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/4281842818Dickson curvesJavier Gomez-Calderon0Department of Mathematics, The Pennsylvania State University, New Kensington Campus, New Kensington 15068, PA, USALet kq denote the finite field of order q and odd characteristic p. For a∈kq, let gd(x,a) denote the Dickson polynomial of degree d defined by gd(x,a)=∑i=0[d/2]d/(d−i)(d−ii)(−a)ixd−2i. Let f(x) denote a monic polynomial with coefficients in kq. Assume that f2(x)−4 is not a perfect square and gcd(p,d)=1. Also assume that f(x) and g2(f(x),1) are not of the form gd(h(x),c). In this note, we show that the polynomial gd(y,1)−f(x)∈kq[x,y] is absolutely irreducible.http://dx.doi.org/10.1155/IJMMS/2006/42818 |
| spellingShingle | Javier Gomez-Calderon Dickson curves International Journal of Mathematics and Mathematical Sciences |
| title | Dickson curves |
| title_full | Dickson curves |
| title_fullStr | Dickson curves |
| title_full_unstemmed | Dickson curves |
| title_short | Dickson curves |
| title_sort | dickson curves |
| url | http://dx.doi.org/10.1155/IJMMS/2006/42818 |
| work_keys_str_mv | AT javiergomezcalderon dicksoncurves |