Now showing items 1-5 of 5
Maps between curves and arithmetic obstructions
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 ...
Maximal differential uniformity polynomials
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.
Tate-Shafarevich groups of constant elliptic curves and isogeny volcanos
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.
Value sets of sparse polynomials
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
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 ...