turkmath.org

I will discuss my joint work with Jori Merikoski and Joni Teräväinen where we develop a sieve that can detect primes in multiplicatively structured sets under certain conditions. In particular, I will discuss the following two applications: a new L-function free approach to Linnik’s problem of bounding the least prime p such that p ≡ a (mod q) (obtaining the bound p « q^{350}) and a new L-function free proof that the interval (x−x^{39/40}, x] contains primes for every large x.
 

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