Ternary quadratic forms that represent zero: the function field case
Terne di quadrati consecutivi in un campo di Galois
Explicit formulae for the number of triplets of consecutive squares in a Galois field are given.
The Brauer-Siegel theorem for algebraic function fields.
The cyclotomic numbers of order eleven
The degree of the splitting field of a random polynomial over a finite field.
The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives
We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.
The distribution of polynomials over finite fields
The distribution of polynomials over finite fields, II
The distribution of r-th powers in a finite field.
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 eleventh power character of 2.
The exponent of class groups on congruence function fields
The factorization of over a finite field where is of first degree and L(x) is linear
The factorization of the derivative of Dickson polynomials.
The Farey Series of polynomials over a finite field.
The fluctuations in the number of points on a family of curves over a finite field
Let be a positive integer, a finite field of cardinality with . In this paper, inspired by [6, 3, 4] and using a slightly different method, we study the fluctuations in the number of -points on the curve given by the affine model , where is drawn at random uniformly from the set of all monic -th power-free polynomials of degree as . The method also enables us to study the fluctuations in the number of -points on the same family of curves arising from the set of monic irreducible...
The formulas for the coefficients of the sum and product of p-adic integers with applications to Witt vectors
The fraction of subspaces of with a specified number of minimal weight vectors is asymptotically Poisson.
The fundamental theorem of prehomogeneous vector spaces modulo (With an appendix by F. Sato)
For a number field with ring of integers , we prove an analogue over finite rings of the form of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where is a big enough prime ideal of and . In the appendix, F.Sato gives an application of the Theorems 1.1, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [Character sums associated to prehomogeneous vector spaces, Compos. Math., 113(1998), 237–346] to the functional equation of -functions...