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# Linnik’s problems and maximal entropy methods

• Andreas Wieser
Article

## 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 et al. (Enseign. Math. 58, 249–313, 2012).

## Keywords

Homogeneous dynamics Equidistribution Quadratic forms

## Mathematics Subject Classification

Primary 37A99 Secondary 11E29

## Notes

### Acknowledgements

This project started with my master thesis. I would like to thank Manfred Einsiedler for suggesting the topic and for many enthusiastic discussions as well as Menny Akka and Manuel Lüthi for commenting on preliminary versions of this paper. I am also very grateful towards the anonymous referee for suggesting a clean proof of Proposition 6.3 and a much improved and generalized exposition of the article.

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## Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

## Authors and Affiliations

• Andreas Wieser
• 1
1. 1.Departement MathematikETH ZürichZurichSwitzerland