Bounded gaps between primes via APs with partly smooth moduli
Julia Stadlmann (University of Illinois at Urbana-Champaign)
Abstract: Following Yitang Zhang's breakthrough on bounded gaps between primes, the Polymath project proved that there are infinitely many prime gaps which are no larger than 246. In this talk I will discuss how the Bombieri-Vinogradov theorem can be combined with newer equidistribution estimates for smooth moduli to obtain small improvements on this result. A key ingredient is a new choice of support for the functions appearing in the corresponding optimization problem for the GPY sieve. To choose this support, we produce various new equidistribution conditions for moduli with a large smooth factor, and reduce the calculation of relevant integrals to repeated matrix multiplication.
algebraic geometrynumber theory
Audience: researchers in the topic
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