Primes in arithmetic progressions to smooth moduli: A minorant version

TL;DR

This paper constructs a minorant function for the prime indicator that has improved distribution properties in arithmetic progressions to smooth moduli, refining previous results.

Contribution

It introduces a new minorant function for primes with enhanced distribution level in arithmetic progressions to smooth moduli, advancing analytic number theory techniques.

Findings

Established a minorant function with distribution level 10/19

Refined previous bounds by Baker--Irving and Stadlmann

Enhanced understanding of prime distribution in smooth moduli arithmetic progressions

Abstract

The author prove that there exists a function $\rho(n)$ which is a minorant for the prime indicator function $\mathbb{1}_{p}(n)$ and has distribution level $\frac{10}{19}$ in arithmetic progressions to smooth moduli. This refines the previous results of Baker--Irving and Stadlmann.