The -invariance of the Potts Hamiltonian.
The geometry of the third moment of exponential sums
We give a geometric interpretation (and we deduce an explicit formula) for two types of exponential sums, one of which is the third moment of Kloosterman sums over of type . We establish a connection between the sums considered and the number of -rational points on explicit smooth projective surfaces, one of which is a surface, whereas the other is a smooth cubic surface. As a consequence, we obtain, applying Grothendieck-Lefschetz theory, a generalized formula for the third moment of Kloosterman...
The irreducibility of compositions of linear polynomials over a finite field
The joint distribution of -additive functions on polynomials over finite fields
Let be a finite field and a polynomial of positive degree. A function on is called (completely) -additive if , where and . We prove that the values are asymptotically equidistributed on the (finite) image set
The number of matrix fields over GF(q)
The number of permutation binomials over where and are primes.
The number of points on certain families of hypersurfaces over finite fields
The number of solutions of certain equations over a finite field
The number of zeroes of x3 + y3 + cz3 in certain finite fields.
The radical factors of over finite fields.
The reduced ideals of a special order in a pure cubic number field
Let be a pure cubic field, with , where is a cube-free integer. We will determine the reduced ideals of the order of which coincides with the maximal order of in the case where is square-free and .
The strong primitive normal basis theorem
The structure of second order sequences in a finite field.
Théorème de Pólya en caractéristique finie
Théorème des deux carrés dans un anneau de polynômes
Théorèmes de densité dans
Thompson's Problem (... =3).
Trace-compatible polynomial sequences over finite fields. (Spur-kompatible Polynomfolgen über endlichen Körpern.)
Transcendence, automata theory and gamma functions for polynomial rings
Transformation de Fourier homogène
Dans leur démonstration de la correspondance de Drinfeld-Langlands, Frenkel, Gaitsgory et Vilonen utilisent la transformation de Fourier géométrique, ce qui les oblige à travailler soit avec les faisceaux -adiques en caractéristique , soit avec les -Modules en caractéristique . En fait, ils n’utilisent cette transformation de Fourier géométrique que pour des faisceaux homogènes pour lesquels on s’attend à avoir une transformation de Fourier sur . L’objet de cette note est de proposer une telle...