题目: Higher uniformity of arithmetic functions in short intervals

报告人：邵烜程,肯塔基大学

时间：4月10日星期三 16:00-16:50

地点：五教 5106

摘要: We study higher uniformity of the Mobius function, the von Mangodt function, and the divisor function on short intervals (X,X+H] where H=X^θ. For example, we prove that for the Mobius function μ and any fixed nilsequence ψ(n), we have ∑_(X≤n<X+H)μ(n)ψ(n)≪H(logX) ^(-A)  for any A>0, provided that θ>5/8. As a consequence, we prove that the Gowers norm of the Mobius function on these short intervals is asymptotically small. As an application, we deduce an asymptotic formula for the number of solutions to linear equations in primes in short intervals. This is joint work with Kaisa Matomaki, Terence Tao, Joni Teravainen.