The Generalized Ramanujan Conjectures and Applications (Lecture 3) by Peter Sarnak
1,105 views · Published 28 March 2013 · 1:15:10 · Indexed 26 October 2026
Channel: International Centre for Theoretical Sciences · 2013 · Science & Technology
Lecture 3: Mobius Randomness and Horocycle Dynamics Abstract : 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". Date: 23 May 2012
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