Abstract
Measure rigidity is a branch of ergodic theory that has recently contributed to the solution of some fundamental problems in number theory and mathematical physics. Examples are proofs of quantitative versions of the Oppenheim conjecture (Eskin et al., 1998), related questions on the spacings between the values of quadratic forms (Eskin et al., 2005; Marklof, 2003; Marklof, 2002), a proof of quantum unique ergodicity for certain classes of hyperbolic surfaces (Lindenstrauss, 2006), and an approach to the Littlewood conjecture on the nonexistence of multiplicatively badly approximable numbers (Einsiedler et al., 2006).
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Marklof, J. (2007). DISTRIBUTION MODULO ONE AND RATNER’S THEOREM. In: Granville, A., Rudnick, Z. (eds) Equidistribution in Number Theory, An Introduction. NATO Science Series, vol 237. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5404-4_11
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