Daniel Di Benedetto

collaborators

3 papers

math.CO2020

Combinatorics of intervals in the plane I: trapezoids

Daniel Di Benedetto, Jozsef Solymosi, Ethan White

We study arrangements of intervals in $R^{2}$ for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic…

math.NT2020

New estimates for exponential sums over multiplicative subgroups and intervals in prime fields

Daniel di Benedetto, Moubariz Z. Garaev, Víctor C. García +3

Let $H$ be a multiplicative subgroup of $F_{p}^{*}$ of order $H > p^{1/4}$ . We show that $$ \max_{(a,p)=1}\left|\sum_{x\in {\mathcal H}} {\mathbf{\,e}}_p(ax)\right| \…

math.CO2020

On the directions determined by a Cartesian product in an affine Galois plane

Daniel Di Benedetto, Jozsef Solymosi, Ethan P. White

We prove that the number of directions contained in a set of the form $A \times B \subset A G (2, p)$ , where $p$ is prime, is at least $∣ A ∣∣ B ∣ - min {∣ A ∣, ∣ B ∣} + 2$ . Here $A$ and $B$ …