## Search

Now showing items 1-5 of 5

#### Maximal differential uniformity polynomials

(2017)

We provide an explicit infinite family of integers m such
that all the polynomials of F2n [x] of degree m have maximal differential
uniformity for n large enough. We also prove a conjecture of the third
author in these cases.

#### Maps between curves and arithmetic obstructions

(2017)

Let X and Y be curves over a finite field. In this article we explore methods
to determine whether there is a rational map from Y to X by considering
L-functions of certain covers of X and Y and propose a specific family ...

#### Value sets of sparse polynomials

(2018)

We obtain a new lower bound on the size of value set V (ƒ) = ƒ(Fp) of a sparse
polynomial ƒ ϵ Fp[X] over a finite field of p elements when p is prime. This
bound is uniform with respect of the degree and depends on some ...

#### Binomial exponential sums

(2018)

We obtain new bounds of exponential sums modulo a prime p with binomials
axk + bxn. In particular, for k=1, we improve the bound of Karatsuba
(1967) from O(n1/4 p3/4) to O(p3/4 + n1/3 p2/3)
for any n, and then use it ...

#### Tate-Shafarevich groups of constant elliptic curves and isogeny volcanos

(2019)

We describe the structure of Tate-Shafarevich groups of a constant elliptic curves over function fields by exploiting the volcano structure of isogeny graphs of elliptic curves over finite fields.