题目：The distribution of squarefree integers in short intervals

主讲人：Ofir Gorodetsky （Oxford）

摘要：The squarefree integers are divisible by no square of a prime. It is well known that they have a positive density within the integers. We consider the number of squarefree integers in a random interval of size H: # {n in [x,x+H] : n squarefree}, where x is a random number between 1 and X. The variance of this quantity has been studied by R. R. Hall in 1982, obtaining asymptotics in the range H < X^{2/9}, with a proof method that stays in 'physical space'. Keating and Rudnick recently conjectured that his result persists for the entire range H < X^{1-epsilon}. We make progress on this conjecture, with properties of Dirichlet polynomials playing a role in our results. We will show how one can verify the conjecture for H slightly beyond X^{1/2}. This is joint work with Kaisa Matomäki, Maks Radziwill and Brad Rodgers.

时间：2020年11月03日，14:00-15:00

地点：腾讯会议，会议 ID：995 338 269