Abstract
AbstractWe 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 is a large modulus, then any invertible residue class mod contains a product of three primes where each prime is at most . 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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