1998
DOI: 10.2307/120984
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Upper Bounds and Asymptotics in a Quantitative Version of the Oppenheim Conjecture

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Cited by 169 publications
(273 citation statements)
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“…Recall that in [EMM,Th. 2.3] we proved that for Q of signature (p, q) with p ≥ 3 and q ≥ 1, and as long as Q is not proportional to a rational form (so that SO(Q)Λ is not closed), and for any continuous function ν on K, we have…”
Section: The Restriction Of B To L Is Identically 0 If and Only Ifmentioning
confidence: 99%
See 2 more Smart Citations
“…Recall that in [EMM,Th. 2.3] we proved that for Q of signature (p, q) with p ≥ 3 and q ≥ 1, and as long as Q is not proportional to a rational form (so that SO(Q)Λ is not closed), and for any continuous function ν on K, we have…”
Section: The Restriction Of B To L Is Identically 0 If and Only Ifmentioning
confidence: 99%
“…This was used to obtain the main result [EMM,Th. 2.1] (which is restated as Theorem 1.1 in the present paper).…”
Section: The Restriction Of B To L Is Identically 0 If and Only Ifmentioning
confidence: 99%
See 1 more Smart Citation
“…Hence sets D 0 = A 0 × B 0 where the closure of A 0 has small Lebesgue measure have small probability, and we can thus remove such sets from the D i . This explains why, without loss of generality, we may assume from now on that the A i are convex and that the hyperplane 8) and write q = m(1, …”
Section: Theorem 41 Assume the Random Field η Is Mixing Of All Ordermentioning
confidence: 99%
“…If the space X is homogeneous, then the weak convergence of the spherical average P t can be proved for all x 0 , with a complete classification of all limit measures, by means of measure rigidity techniques that are based on Ratner's measure classification theorem for subgroups generated by unipotent elements [22]. There is now a large body of literature on this topic, see for instance [7,8,16,17,19,24]. In some settings, spherical equidistribution may also be deduced directly from the mixing property of R [7].…”
mentioning
confidence: 99%