Gaussian sums over finite fields and gamma functions. (Gaussche Summen über endlichen Körpern und Gammafunktion.)
Généralisation d'un théorème de I. M. Vinogradov à un corps de séries formelles sur un corps fini
Generalizations of the classical Chebyshev polynomials to polynomials in two variables
Generalized Jacobsthal sums and sums of squares
Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication
A fractional differential controller for incommensurate fractional unified chaotic system is described and proved by using the Gershgorin circle theorem in this paper. Also, based on the idea of a nonlinear observer, a new method for generalized synchronization (GS) of this system is proposed. Furthermore, the GS technique is applied in secure communication (SC), and a chaotic masking system is designed. Finally, the proposed fractional differential controller, GS and chaotic masking scheme are...
Generating linear spans over finite fields
GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation
The Legendre symbol has been used to construct sequences with ideal cross-correlation, but it was never used in the arithmetic cross-correlation. In this paper, a new class of generalized Legendre sequences are described and analyzed with respect to their period, distributional, arithmetic cross-correlation and distinctness properties. This analysis gives a new approach to study the connection between the Legendre symbol and the arithmetic cross-correlation. In the end of this paper, possible application...
Graphes de Ramanujan et applications
Green-Tao theorem in function fields
Groupes de Witt d'un corps de caractéristique 2.
Groups and Fields in Zn.
Hauteurs canoniques et modules de Drinfeld.
Heights in finite projective space, and a problem on directed graphs.
Hyperquadratic power series of degree four
Improvements on the Cantor-Zassenhaus factorization algorithm
The paper presents a careful analysis of the Cantor-Zassenhaus polynomial factorization algorithm, thus obtaining tight bounds on the performances, and proposing useful improvements. In particular, a new simplified version of this algorithm is described, which entails a lower computational cost. The key point is to use linear test polynomials, which not only reduce the computational burden, but can also provide good estimates and deterministic bounds of the number of operations needed for factoring....
Incomplete character sums and a special class of permutations
We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an -orthomorphism. Examples of -orthomorphisms are given.
Incomplete character sums over finite fields and their application to the interpolation of the discrete logarithm by Boolean functions
Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators
Indépendance algébrique de certaines séries formelles
Infinitude of Wilson primes for