A conjecture of Erdős states that for every large enough prime q, every reduced residue class modulo q is the product of two primes less than q. I will discuss my on-going work with Kaisa Matomäki establishing among other things a ternary variant of Erdős’ conjecture, namely that every reduced residue class modulo q is the product of three primes less than q. The proof is based on a multiplicative transference principle, Kneser’s theorem, and bounds for the least primes in cosets of small index subgroups.
This video is part of the Institute for Advanced Study‘s Special year research seminar.
