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math.NT2008
On Katz's bound for number of elements with given trace and norm
Marko Moisio, Daqing Wan
In this note an improvement of the Katz's bound on the number of elements in a finite field with given trace and norm is given. The improvement is obtained by reducing the problem…
math.NT2007★ 8 cited
Irreducible polynomials with prescribed trace and restricted norm
K. Kononen, M. Moisio, M. Rinta-aho +1
Let GF(q), q=p^r, be a finite field with a primitive element g. In this paper we use exponential sums and Jacobi sums to compute the number of the irreducible polynomials of degree…
math.NT2007
Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed
M. Moisio, K. Ranto
Let be a finite field of characteristic . We give the number of irreducible polynomials $x^m+a_{m-1}x^{m-1}+...+a_0\in\F_q[x]$ with and prescribed…