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. 
Gary McGuire, Emrah Sercan Y{\i}lmaz
math.AG