A class of permutation trinomials over finite fields
Let q > 2 be a prime power and , where . We prove that f is a permutation polynomial of if and only if one of the following occurs: (i) q is even and ; (ii) q ≡ 1 (mod 8) and t² = -2.
A Goldbach theorem for polynomials of low degree over odd finite fields
A lower bound theorem in Fq[x].
A method for solving equations in finite fields
A notion of density and essential components in GF[p,x]
A polynomial representation for logarithms in GF(q)
A quick and dirty irreducibility test for multivariate polynomials over .
Addition theorems in F q [x].
Addition theorems in Fq [x].
An analogue of the Erdős-Ginzburg-Ziv theorem for quadratic symmetric polynomials.
Arithmetical properties of function fields (II). The generalized Schur problem
Bases for integer-valued polynomials in a Galois field
Chebyshev polynomials in several variables.
Classification of irreducible factorable polynomials over a finite field
Constructing irreducible polynomials with prescribed level curves over finite fields.
Corps fini ou champ de Galois
Corrections to "Irreducibility of the iterates of a quadratic polynomial over a field" (Acta Arith. 93 (2000), 87-97)
Correspondences in a finite field, I
Counting irreducible polynomials over finite fields
In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: where denotes the number of monic irreducible polynomials in with norm .
Counting monic irreducible polynomials in for which order of is odd
Hasse showed the existence and computed the Dirichlet density of the set of primes for which the order of is odd; it is . Here we mimic successfully Hasse’s method to compute the density of monic irreducibles in for which the order of is odd. But on the way, we are also led to a new and elementary proof of these densities. More observations are made, and averages are considered, in particular, an average of the ’s as varies through all rational primes.