Exponential Sums over Points of Elliptic Curves

TL;DR

This paper introduces a new bound for bilinear exponential sums over elliptic curve points, leading to improved results in related exponential sum estimates and elliptic curve arithmetic problems.

Contribution

It presents a novel bound for bilinear sums over elliptic curve points, enhancing previous results in exponential sum estimates and elliptic curve arithmetic.

Findings

Improved bounds for exponential sums over elliptic curves

Enhanced results in elliptic curve arithmetic problems

Stronger estimates for bilinear sums involving elliptic curve points

Abstract

We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on elliptic curves.