Toward a theory of prime detecting sieves
Toward a theory of prime detecting sieves
In-Person and Online Talk
Meeting ID:听 920 2195 5230
Passcode:听 听 The three-digit integer that is the cube of the sum of its digits.听
Given a set of integers, we wish to know how many primes听there are in the set.听 Modern tools allow us to obtain an asymptotic for the number of primes, or at least a lower bound of the expected order, assuming certain strength Type-I information (the distribution of the sequence in progressions) and Type-II information (bilinear sums over the sequence).听The methods used previously, especially Harman's sieve, are largely ad-hoc and shed little light on the limitations of the methods. In joint work with James Maynard, we develop a systematic framework for understanding the theoretical limits of these prime detecting sieves, which allow us, in principle, to answer these questions for any given Type I and Type-II information.