Lyosha Klurman: Mean values of multiplicative functions over the function fields

Understanding mean values and correlations of multiplicative functions over
number fields plays key role in analytic number theory.
Motivated by the recent work of Granville, Harper and Soundararajan we discuss
mean values of multiplicative functions over the function fields \mathbb{F}_q
[x]. In particular, we prove stronger function field analogs of several
classical results due to Wirsing, Halasz, Hall, Tenenbaum explaining some
surprising features that are not present in the number field setting. Our main
result describes spectrum of multiplicative functions over the function
fields. This is based on joint works with K. Soundararajan and C. Pohoata.