A Bombieri -- Vinogradov type result for exponential sums over Piatetski-Shapiro primes

TL;DR

This paper proves a Bombieri--Vinogradov type theorem for exponential sums over Piatetski-Shapiro primes within a specific range of the parameter gamma, advancing understanding of their distribution.

Contribution

It establishes a new Bombieri--Vinogradov type result specifically for exponential sums over Piatetski-Shapiro primes, a class of primes defined by fractional power sequences.

Findings

Proves a Bombieri--Vinogradov type theorem for Piatetski-Shapiro primes

Extends distribution results to exponential sums over these primes

Focuses on the range 865/886 < gamma < 1

Abstract

In this paper, we establish a theorem of Bombieri -- Vinogradov type for exponential sums over Piatetski-Shapiro primes $p= [n^{1/\gamma}]$ with $\frac{865}{886}<\gamma < 1$.