IRREDUCIBLE POLYNOMIALS WITH PRESCRIBED TRACE AND RESTRICTED NORM
Let
be a finite field with a primitive element
In this paper we use exponential sums and Jacobi sums to compute the number of the irreducible polynomials of degree m over
with trace fixed and norm restricted to a coset of a subgroup
We give the number explicitly for
and for
when
.
irreducible polynomials, monomial exponential sums, Gauss sums, Jacobi sums.
