Primes in arithmetic progressions to smooth moduli: A minorant version

Abstract

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

6 pages. Corrected an error in the proof