Approaching the two-point Chowla conjecture via matrices

Seminar series

Random Matrix Theory Seminars

Date

Tue, 20 May 2025
16:00

Location

Speaker

Cedric Pilatte

Organisation

University of Oxford

The two-point Chowla conjecture predicts that $\sum_{x<n<2x} \lambda(n)\lambda(n+1) = o(x)$ as $x\to \infty$ , where $\lambda$ is the Liouville function (a $\{\pm 1\}$ -valued multiplicative function encoding the parity of the number of prime factors). While this remains an open problem, weaker versions of this conjecture are known. In this talk, we outline an approach initiated by Helfgott and Radziwill, which reformulates the problem in terms of bounding the eigenvalues of a certain matrix.