Neo Tardy

Two-point correlations of multiplicative functions with dense orbits 

Let f and g be two completely multiplicative functions taking values on the unit circle, and assume that their images are dense. Since n and n+1 are coprime, one could expect the functions f(n) and g(n+1) to have independent behaviors. In particular, one could conjecture that the image of (f(n),g(n+1)) is dense in the torus. However, f and g can sometimes be correlated through an analytic structure, leading to counterexamples to this conjecture, as identified by Klurman and Mangerel. The aim of this talk is to discuss the main ideas of their proof, as well as discuss an extension to a stronger result on the distribution of (f(n),g(n+1)) on the torus.