A new bound for the large sieve inequality with power moduli

TL;DR

This paper introduces a novel bound for the large sieve inequality involving power moduli q^k, providing a uniform result across different values of k, utilizing a new theorem from Wooley's efficient congruencing work.

Contribution

It presents a new, uniform bound for the large sieve inequality with power moduli, leveraging recent advances in efficient congruencing.

Findings

Established a new bound for the large sieve with power moduli

The bound is uniform in the exponent k

Utilized Wooley's efficient congruencing theorem

Abstract

We give a new bound for the large sieve inequality with power moduli q^k that is uniform in k. The proof uses a new theorem due to T. Wooley from his work on efficient congruencing.