On Exponential Sums in Finite Fields, II.
On linear recursion and pseudorandomness
On sums and products of residues modulo p
On the concentration of points on modular hyperbolas and exponential curves
On the cycle structure of linear recurring sequences.
On the degree of the -function associated with an exponential sum
On the distribution of distances between the points of affine curves over finite fields.
On the estimation of certain exponential sums
On the number of orthogonal systems in vector spaces over finite fields.
On the -adic continuation of the logarithmic derivative of certain hypergeometric functions
On the set .
On the set of distances between two sets over finite fields.
On the special solutions of an equation in a finite field.
On zero-testing and interpolation of sums of characters.
-adic estimates for exponential sums and the theorem of Chevalley-Warning
Period polynomials and Gauss sums for finite fields
Poids des duaux des codes BCH de distance prescrite et sommes exponentielles
Soit un entier pair. On considère un code BCH binaire de longueur et de distance prescrite avec . Le poids d’un mot non nul du dual de peut s’exprimer en fonction d’une somme exponentielle. Nous montrerons que cette somme n’atteint pas la borne de Weil et nous proposerons une amélioration de celle-ci. En conséquence, nous obtiendrons une amélioration de la borne de Carlitz-Uchiyama sur le poids des mots du dual de .
Poids des duaux des codes BCH de distance prescrite et sommes exponentielles
Power-moments of SL Kloosterman sums
Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL have been considered, in which analogous GL-Kloosterman sums (related to the corresponding Bruhat decomposition) appear. In this note we investigate the first four power-moments of the Kloosterman sums associated with the group SL. We give formulas for the...
Proof of a conjectured three-valued family of Weil sums of binomials
We consider Weil sums of binomials of the form , where F is a finite field, ψ: F → ℂ is the canonical additive character, , and . If we fix F and d, and examine the values of as a runs through , we always obtain at least three distinct values unless d is degenerate (a power of the characteristic of F modulo ). Choices of F and d for which we obtain only three values are quite rare and desirable in a wide variety of applications. We show that if F is a field of order 3ⁿ with n odd, and with...