Oleksiy Klurman

Oleksiy Klurman, KTH Royal Institute of Technology, Stockholm, SUÈDE

Joint distribution of multiplicative functions

Understanding the joint behaviour of (f(n), g(n+1)), where f and g are given multiplicative functions, play a key role in analytic number theory
with potentially profound consequences such as Riemann hypothesis, twin prime conjecture, Chowla's conjecture and many others.

I will discuss how one can combine recent breakthroughs by Matomaki-Radziwiłł and Tao together with some ideas from additive combinatorics
to answer an old question of Katai about distribution of points {(f(n), g(n+1))}n ≥ 1 in C2, where f and g are multiplicative functions.

This talk is based on a joint work with A. Mangerel.