Higher order uniformity of the Möbius function

Joint IAS/Princeton University Number Theory Seminar
Topic:Higher order uniformity of the Möbius function
Speaker:Joni Teräväinen
Affiliation:University of Oxford
Date:Thursday, December 5
Time/Room:4:30pm - 5:30pm/Princeton University, Fine 214

In a recent work, Matomäki, Radziwill and Tao showed that the Möbius function is discorrelated with linear exponential phases on almost all intervals of length $X^{\varepsilon}$. I will discuss joint work where we generalize this result to nilsequences, so as a special case the Möbius function is shown not to correlate with polynomial phases on almost all intervals of length $X^{\varepsilon}$. As an application, we show that the number of sign patterns of length $k$ that the Liouville function takes grows superpolynomially in $k$.