The distribution of periodic torus orbits on homogeneous spaces
By Manfred Einsiedler, Elon Lindenstrauss, P. Michel, Akshay Venkatesh. 2006
82 citations recorded by the source corpus.
We prove results towards the equidistribution of certain families of periodic torus orbits on homogeneous spaces, with particular focus on the case of the diagonal torus acting on quotients of PGLn(R). After attaching to each periodic orbit an integral invariant (the discriminant) our results have the following flavour: certain standard conjectures about the distribution of such orbits hold up to exceptional sets of at most O(� ǫ ) orbits of discriminant ≤ �. The proof relies on the well-separatedness of periodic orbits together with measure rigidity for torus actions. We also give examples of sequences of periodic orbits of this action that fail to become equidistributed, even in higher rank. We give an application of our results to sharpen a theorem of Minkowski on ideal classes in totally real number fields of cubic and higher degrees.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/87a0f5633f8c83e36f0d63b2dea535eb5d45b6e8
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In Geometry and Topology
- Akshay Venkatesh
- P. Michel
- Manfred Einsiedler
- D. Whitehouse
- Kimball Martin
- Gregory Margulis
- V. Blomer
- R. Munshi
In Mathematical Physics
- Akshay Venkatesh
- P. Michel
- Manfred Einsiedler
- Gregory Margulis
- D. Whitehouse
- Kimball Martin
- V. Blomer
- M. Young
Citations in the corpus
- Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces (2007, methodology): “[ 18 ]). In arithmetic applications, what one can easily measure is the discriminant, rather than the volume, of a closed H-orbit; thus we shall present a proposition relating the two.”
- Central L-Values and Toric Periods for GL(2) (2009, background): “) We remark that in general one needs some condition, such as the one above on the growth of the class number, to ensure equidistribution of individual geodesics (see [4]).”
- The subconvexity problem for GL2 (2009, background): “[20], footnote 15 for a proof in the case of real groups, from which the stated result is easily deduced.”