Oleksiy Klurman

Max Planck Institute, Bonn

Small discrepancy sequences over Fq[x]

Heilbronn Number Theory Seminar
12th February 2020, 4:00 pm – 5:00 pm
Fry Building, 2.04

The famous Erdos discrepancy problem (now a theorem due to Tao) asserts that for any sequence a_n of +/- 1s we have sup_{n, d} |\sum_{k=0}^n a_kn| = infinity.

It was observed during the Polymath5 project that the analogous statement over the polynomial ring Fq[x] is false. In this talk, I will describe corrected" form of the EDP over Fq[x], focusing on some features that are not present in the number field setting.

In particular, I will describe the proof of the function field version of the following number field conjecture: completely multiplicative functions￼ on the integers which take only the values +/- 1 with the smallest possible discrepancy are the "modified characters."

This is based on a joint work with A. Mangerel (CRM) and J. Teravainen (Oxford).