Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik
By P. Michel, Akshay Venkatesh. 2006
94 citations recorded by the source corpus.
An old question of Linnik asks about the equidistribution of integral points on a large sphere. This question proved to be very rich: it is intimately linked to modular forms, to subconvex estimates for L-functions, and to dynamics of torus actions on homogeneous spaces. Indeed, Linnik gave a partial answer using ergodic methods, and his question was completely answered by Duke using harmonic analysis and modular forms. We survey the context of these ideas and their developments over the last decades.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7417713f51417a08dea8b1b70105d458de6013f7
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In Algebra and Number Theory
- V. Blomer
- Akshay Venkatesh
- P. Michel
- Gergely Harcos
- R. Munshi
- Manfred Einsiedler
- M. Young
- D. Whitehouse
In Geometry and Topology
- Akshay Venkatesh
- Manfred Einsiedler
- V. Blomer
- P. Michel
- Gergely Harcos
- Elon Lindenstrauss
- Y. Benoist
- D. Whitehouse
In Mathematical Physics
- Akshay Venkatesh
- P. Michel
- V. Blomer
- Manfred Einsiedler
- Gergely Harcos
- Elon Lindenstrauss
- R. Munshi
- M. Young
Citations in the corpus
- Central L-Values and Toric Periods for GL(2) (2009, background): “[4] Einseidler, M., E. Lindenstrauss, P. Michel, and A. Venkatesh.”
- The subconvexity problem for GL2 (2009, methodology): “in [50]) of some of the results of this paper and its appearance.”
- Effective equidistribution of S-integral points on symmetric varieties (2007, background): “We refer to [35], [29], [23], [20], [28], [18], [41] etc.”
- Distribution of periodic torus orbits and Duke's theorem for cubic fields (2007, background): “Each of these papers is self-contained and can be read independently; related discussions can also be found in [16, 36].”
- Bounds for modular $L$-functions in the level aspect (2007, background): “For many obvious (e.g. bounding contour integrals) and not so obvious (e.g. equidistribution problems) applications it turns out to be crucial to have estimates for the size of L-functions inside the critical strip, and without much loss of generality on the critical line Re s = 12 .”