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Asymptotic distribution of values of isotropic quadratic forms at S-integral points
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Han, Jiyoung | - |
dc.contributor.author | Lim, Seonhee | - |
dc.contributor.author | Mallahi-Karai, Keivan | - |
dc.date.accessioned | 2023-07-14T04:17:27Z | - |
dc.date.available | 2023-07-14T04:17:27Z | - |
dc.date.created | 2018-11-08 | - |
dc.date.issued | 2017-01 | - |
dc.identifier.citation | Journal of Modern Dynamics, Vol.11, pp.501-550 | - |
dc.identifier.issn | 1930-5311 | - |
dc.identifier.uri | https://hdl.handle.net/10371/195150 | - |
dc.description.abstract | We prove an analogue of a theorem of Eskin-Margulis-Mozes [10]. Suppose we are given a finite set of places S over Q containing the Archimedean place and excluding the prime 2, an irrational isotropic form q of rank n≥4 on QS, a product of p-adic intervals Ip, and a product ω of star-shaped sets. We show that unless n ≥ 4 and q is split in at least one place, the number of S-integral vectors v ∈ TΩ satisfying simultaneously q(v) ∈ Ip for p ∈ S is asymptotically given by λ(q,ω)|I|·||T||n-2 as T goes to infinity, where |I| is the product of Haar measures of the p-adic intervals Ip. The proof uses dynamics of unipotent flows on S-arithmetic homogeneous spaces; in particular, it relies on an equidistribution result for certain translates of orbits applied to test functions with a controlled growth at infinity, specified by an S-arithmetic variant of the α-function introduced in [10], and an S-arithemtic version of a theorem of Dani-Margulis [7]. © 2017 AIMSCIENCES. | - |
dc.language | 영어 | - |
dc.publisher | American Institute of Mathematical Sciences | - |
dc.title | Asymptotic distribution of values of isotropic quadratic forms at S-integral points | - |
dc.type | Article | - |
dc.identifier.doi | 10.3934/jmd.2017020 | - |
dc.citation.journaltitle | Journal of Modern Dynamics | - |
dc.identifier.wosid | 000416734400002 | - |
dc.identifier.scopusid | 2-s2.0-85032801001 | - |
dc.citation.endpage | 550 | - |
dc.citation.startpage | 501 | - |
dc.citation.volume | 11 | - |
dc.description.isOpenAccess | Y | - |
dc.contributor.affiliatedAuthor | Lim, Seonhee | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.subject.keywordPlus | HOMOGENEOUS SPACES | - |
dc.subject.keywordPlus | FLOWS | - |
dc.subject.keywordAuthor | Oppenheim conjecture | - |
dc.subject.keywordAuthor | homogeneous dynamics | - |
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