On irreducible polynomials of certain types in finite fields
Stephen D. Cohen · Mathematical Proceedings of the Cambridge Philosophical Society · 1969
LetGF(q) be the finite field containingq=plelements, wherepis a prime andla positive integer. LetP(x)be a monic polynomial inGF[q, x] of degreem. In this paper we investigate the nature and distribution of monic irreducible polynomials of the following types: (I)P(xr), whereris a positive integer (r-polynomials). (II)xmP(x+x−1). (Reciprocal polynomials.) These have the form (III)xrmP(xr+x−r). (r-reciprocal polynomials.) These have the formQ(xr), whereq(x) satisfies (1·1).