Number Theory Seminar

Sacha Mangarel, Centre de Recherches Mathématiques

"On Low Discrepancy Multiplicative Sequences"

The Erdos Discrepancy Problem, now a theorem due to Tao, states that any completely multiplicative function f: \mathbb{N} \rightarrow \{-1,+1\} has unbounded partial sums. It is natural to ask whether there is a minimal rate of growth for these partial sums, and Tao has conjectured such a rate of growth, as well as a class of extremal examples. In this talk we will explain his conjecture, and outline a proof of its analogue in the setting of polynomials over finite fields. (Joint work with O. Klurman and J. Teräväinen.)

MC 5417