by
Prof.Peter Sarnak(Princeton University and Institute for Advanced Study, USA)
→
Asia/Kolkata
AG-66 (Colaba Campus)
AG-66
Colaba Campus
Description
The Mobius function mu(n) is minus one to the number of distinct
prime factors of n if n has no square factors and zero otherwise.
Understanding the randomness (often referred to as the `Mobius
randomness principle' in this function is a fundamental and very
difficult problem. We will explain a precise dynamical formulation of
the randomness and report on recent advances establishing it. In
particular the disjointness of the resulting Mobius Flow from
horocycle flows and related horocycle dynamics at ``prime times''.