Shortest Distance in Modular Cubic Polynomials

Abstract

In this paper, we study how small a box contains at least two points from a modular cubic polynomial $y\equiv a{x}^3+b{x}^2+cx+d(\mathrm{mod}p)$ with $(a,p)=1$. We prove that some square of side length $p^{1/6+\epsilon }$ contains two such points.

3 pages

References in corpus (1)

• Character sums over unions of intervals