Linnik's problems and maximal entropy methods

TL;DR

This paper applies maximal entropy methods to study the distribution of primitive integer points on spheres and CM points on the modular surface, offering a modern dynamical perspective on Linnik's problems.

Contribution

It introduces a dynamical interpretation of Linnik's problems using maximal entropy techniques, building on recent advances by Einsiedler, Lindenstrauss, Michel, and Venkatesh.

Findings

Distribution properties of primitive integer points on spheres analyzed.

Distribution of CM points on the modular surface examined.

Modern dynamical methods provide new insights into classical problems.

Abstract

We use maximal entropy methods to examine the distribution properties of primitive integer points on spheres and of CM points on the modular surface. The proofs we give are a modern and dynamical interpretation of Linnik's original ideas and follow techniques presented by Einsiedler, Lindenstrauss, Michel and Venkatesh in 2011.