### Correlations of multiplicative functions along Beatty sequences

Heilbronn Number Theory Seminar

1st November 2023, 4:00 pm – 5:00 pm

Fry Building, 2.04

Suppose a(n) and b(n) are two increasing sequences of natural numbers. If a(n) and b(n) have 'low complexity' (e.g. are linear, quadratic etc.), a rich vein of recent work considers the multiplicative structure of a(n) and b(n) simultaneously, and asks whether certain asymptotic independence results can be proved. In this talk we will briefly review the bouquet of recent results that are known (for various different sequences a(n) and b(n)), before focusing on the case when a(n) and b(n) are Beatty sequences. We will discuss our recent work with J. Teräväinen on these sequences, resolving a conjecture of Frantzikinakis on two-point correlations (and providing the first non-trivial progress on the higher order cases).

## Comments are closed.