Joint IAS/Princeton University Number Theory Seminar

Topic: Higher order uniformity of the Möbius function

Speaker: Joni Teräväinen

Affiliation: University of Oxford

Date & Time: Thursday December 5th, 2019, 4:30pm - 5:30pm

Location: 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 $k$.