The Ruziewicz problem and distributing points on homogeneous spaces of a compact Lie group (Q814143)

Let \(G\) be a compact non-commutative Lie group not locally isomorphic to \(SO(3)\). This paper provides a generalization of a theorem of Lubotzky, Phillips and Sarnak on distributing points on the sphere \(S^2\) (or \(S^3\)) to any homogeneous space of \(G\). To be more precise, for infinitely many primes \(p\), the author constructs a finite subset \(S_p\), and gives a bound for the operator norm \(\lambda_{S_p}\). The result can be viewed as a quantitative solution to the generalized Ruziewicz problem.