Explicit Factorizations of Cyclotomic and Dickson Polynomials over Finite Fields

We give, over a finite field Fq, explicit factorizations into a product of irreducible polynomials, of the cyclotomic polynomials of order 3·2n, the Dickson polynomials of the first kind of order 3·2n and the Dickson polynomials of the second kind of order 3·2n  − 1

UNAMBIGUOUS EVALUATIONS OF BIDECIC JACOBI AND JACOBSTHAL SUMS

Abstract For a class of primes p = 1 (mod 20) for which 2 is a quintic nonresidue, unambiguous evaluations of parameters of bidecic Jacobi and Jacobsthal sums (modp

Explicit multiplicative relations between Gauss sums

H.Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes