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arXiv · 2208.05762

On the existence of products of primes in arithmetic progressions

Barnabás Szabó
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Abstract

We study the existence of products of primes in arithmetic progressions, building on the work of Ramar\'e 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 $q^{6/5+\epsilon}$. 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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Barnabás Szabó. 2022-08-11. On the existence of products of primes in arithmetic progressions. https://arxiv.org/abs/2208.05762

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