The Number of Irreducible Polynomials with the First Two Coefficients Fixed over Finite Fields of Odd Characteristic

In this paper we give a different proof of Kuz'min's result on the number of irreducible polynomials with the first two coefficients fixed. Our technique is to relate the question to the number of points on a curve, and to calculate the L-polynomial of the curve.
Comment: arXiv admin note: text overlap with arXiv:1605.07229