On fundamental sets over a finite field.
On generalized Redei functions.
On linear recursion and pseudorandomness
On orthogonal systems and permutation polynomials in several variables
On partitions and cyclotomic polynomials.
On perfect polynomials over .
On permutation polynomials over finite fields.
On polynomial Gauss sums (mod Pⁿ), n ≥ 2
On polynomials of the form .
On rationality of Jacobi sums
On real quadratic number fields suitable for cryptography.
On sets of polynomials whose difference set contains no squares
Let be the polynomial ring over the finite field , and let be the subset of containing all polynomials of degree strictly less than N. Define D(N) to be the maximal cardinality of a set for which A-A contains no squares of polynomials. By combining the polynomial Hardy-Littlewood circle method with the density increment technology developed by Pintz, Steiger and Szemerédi, we prove that .
On singular moduli for rank 2 Drinfeld modules
On solutions of polynomial congruences
On Solvability by Radicals of Field Extensions.
On Solvability by Radicals of Finite Fields.
On some equations over finite fields
In this paper, following L. Carlitz we consider some special equations of variables over the finite field of elements. We obtain explicit formulas for the number of solutions of these equations, under a certain restriction on and .
On some Kloosterman sums.
On some permutation polynomials over finite fields.
On some subgroups of the multiplicative group of finite rings
Let be a subset of , the field of elements and a polynomial of degree with no roots in . Consider the group generated by the image of in the group of units of the ring . In this paper we present a number of lower bounds for the size of this group. Our main motivation is an application to the recent polynomial time primality testing algorithm [AKS]. The bounds have also applications to graph theory and to the bounding of the number of rational points on abelian covers of the projective...