On the existence of products of primes in arithmetic progressions

2022/08/11 by Szabó, Barnabás
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2208.05762

Abstract

We study the existence of products of primes in arithmetic progressions, building on the work of Ramaré and Walker. One of our main results is that if q is a large modulus, then any invertible residue class mod q contains a product of three primes where each prime is at most q^6/5+ε. Our arguments use results from a wide range of areas, such as sieve theory or additive combinatorics, and one of our key ingredients, which has not been used in this setting before, is a result by Heath-Brown on character sums over primes from his paper on Linnik's theorem.

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