A conditional result on exponential sums over primes in short intervals

TL;DR

This paper presents a conditional result on exponential sums over primes in short intervals, assuming the truth of the Generalized Riemann Hypothesis and the Density Hypothesis for Dirichlet L-functions.

Contribution

It provides a new conditional estimate for exponential sums over primes in short intervals based on key unproven hypotheses in number theory.

Findings

Conditional bounds on exponential sums over primes

Assumption of GRH and Density Hypothesis leads to these bounds

Enhances understanding of prime distribution in short intervals

Abstract

The aim of this work is to illustrate a conditional result involving the exponential sums over primes in short intervals under the assumption that both the Generalized Riemann Hypothesis and the Density Hypothesis for Dirichlet $L$-functions are true.