Period of a linear recurrence
Permutation matrices and matrix equivalence over a finite field.
Point Sets and Sequences with Small Discrepancy.
Prime k-th power non-residues
Rational approximations to algebraic Laurent series with coefficients in a finite field
We give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of automata theory and, in our context, of a classical theorem due to Christol. We then introduce a new approach which allows us to strongly improve this general bound in many cases. As an illustration, we give a few examples of algebraic Laurent series for which...
Some inequalities in functional analysis, combinatorics, and probability theory.
Some problems in multidimensional analytic number theory
Somme des chiffres et transcendance
Suites récurrentes linéaires en caractéristique non nulle
Sur la forme canonique des congruences du second degré et le nombre de Ieurs solutions.
Symmetry of iteration graphs
We examine iteration graphs of the squaring function on the rings when , for a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when and when and are symmetric when .
Systems of four equations with a matrix application in a finite field
The Brauer-Siegel theorem for algebraic function fields.
The fraction of subspaces of with a specified number of minimal weight vectors is asymptotically Poisson.
The number of matrix fields over GF(q)
The structure of second order sequences in a finite field.
Théorèmes de densité dans
Über den Rang gewisser zirkulanter Matrizen (zu Problem 764A).
Ultraprodukte endlicher Körper.
Value sets of functions over finite fields