Car-Pólya and Gel’fond’s theorems for
Character sums in finite fields
Chebyshev polynomials and Pell equations over finite fields
We shall describe how to construct a fundamental solution for the Pell equation over finite fields of characteristic . Especially, a complete description of the structure of these fundamental solutions will be given using Chebyshev polynomials. Furthermore, we shall describe the structure of the solutions of the general Pell equation .
Chebyshev polynomials in several variables.
Class numbers of cyclotomic function fields
Classes modulo les puissances dans l'anneau des S-entiers d'un corps de fonctions
Classification of irreducible factorable polynomials over a finite field
Closed form expressions for several Ramanujan sums
Cohomologie des fonctions
Common divisors of and over function fields.
Complete arcs arising from a generalization of the Hermitian curve
We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of rational points of a class of Artin-Schreier curves, which is calculated by using exponential sums via Coulter's approach. We also single out some examples of maximal curves.
Complete solution of the cyclotomic problem in for any prime modulus
Congruence properties of the hyperkloosterman sum
Constructing irreducible polynomials with prescribed level curves over finite fields.
Construction of Optimal Linear Codes by Geometric Puncturing
Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4.∗This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 24540138.
Corps fini ou champ de Galois
Correction to "Minimal polynomials for Gauss periods with f=2" (Acta Arith. 121 (2006), 233-257)
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 .