Joni Teräväinen, University of Turku
I will discuss a new sieve that allows detecting primes in sequences that have strong type I information and some multiplicative structure. This allows one to find primes in sequences that have good type I information and a suitable multiplicative structure. While Type I information is not sufficient for detecting primes with a classical sieve, it turns out to be possible to detect them in cases where a multiplicative structure allows one to combine Type I information from different scales. Among other things, the method gives new L-function free proofs of Linnik’s and Hoheisel’s theorems. The talk is based on ongoing joint work with Kaisa Matomäki and Jori Merikoski.