Dickson curves

Javier Gomez-Calderon

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-6

Abstract:

Let k q denote the finite field of order q and oddcharacteristic p . For a ∈ k q , let g d ( x , a ) denote theDickson polynomial of degree d defined by g d ( x , a ) = ∑ i = 0 [ d / 2 ] d / ( d − i ) ( d − i i ) ( − a ) i x d − 2 i . Let f ( x ) denote a monicpolynomial with coefficients in k q . Assume that f 2 ( x ) − 4 is not a perfect square and gcd ⁡ ( p , d ) = 1 . Also assume that f ( x ) and g 2 ( f ( x ) , 1 ) are not of the form g d ( h ( x ) , c ) . In this note, we show that the polynomial g d ( y , 1 ) − f ( x ) ∈ k q [ x , y ] is absolutely irreducible.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:042818

DOI: 10.1155/IJMMS/2006/42818

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