Reduction formulas for certain multiple exponential sums
Remarks on Hua's estimate of complete trigonometrical sums
Sums for U(2n,q²) and their applications
Sums of L-functions over rational function fields
Sur les propriétés de divisibilité des nombres de classes des corps quadratiques
The Divisibility Modulo 4 of Kloosterman Sums over Finite Fields of Characteristic 3
Recently Garashuk and Lisonek evaluated Kloosterman sums K (a) modulo 4 over a finite field F3m in the case of even K (a). They posed it as an open problem to characterize elements a in F3m for which K (a) ≡ 1 (mod4) and K (a) ≡ 3 (mod4). In this paper, we will give an answer to this problem. The result allows us to count the number of elements a in F3m belonging to each of these two classes.
The divisor function over arithmetic progressions
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 number of points on certain families of hypersurfaces over finite fields
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...
Twisted exponential sums and Newton polyhedra.
Twisted exponential sums over points of elliptic curves
Weighted quadratic partitions (mod pr).
Рациональные тригонометрические суммы вдоль кривой