Counting integral points in certain homogeneous spaces
文献类型：期刊论文
| 作者 | Wei, Dasheng1,2 ; Xu, Fei3
|
| 刊名 | JOURNAL OF ALGEBRA
 |
| 出版日期 | 2016-02-15 |
| 卷号 | 448页码:350-398 |
| 关键词 | Integral point Homogeneous space Tamagawa measure |
| ISSN号 | 0021-8693 |
| DOI | 10.1016/j.jalgebra.2015.09.043 |
| 英文摘要 | The leading term of asymptotic formula of the number of integral points in non-compact symmetric homogeneous spaces of semi-simple simply connected algebraic groups is given by the average of the product of the number of local solutions twisted by the Brauer Manin obstruction. The similar result is also true for homogeneous spaces of reductive groups with some restriction. As application, we will give the explicit asymptotic formulae of the number of integral points of certain norm equations and prove the leading term of asymptotic formula of the number of integral matrices with a fixed irreducible characteristic polynomial over Z studied by Eskin Mozes Shah is equal to the product of the number of local integral solutions over all primes although the density function defined by Borovoi and Rudnick is not trivial in general. We also answer a question raised by Borovoi and Rudnick for comparing the number of integral symmetric matrices with the given determinant with the product of local densities. (C) 2015 Elsevier Inc. All rights reserved. |
| 资助项目 | NSFC[10671104] ; NSFC[11031004] ; 973 Program[2013CB834202] ; Deutsche Forschungsgemeinschaft[DE 1646/2-1] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000375634500011 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/22644]  |
| 专题 | 数学所 |
| 通讯作者 | Xu, Fei |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Munich, Math Inst, Theresienstr 39, D-80333 Munich, Germany 3.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China |
| 推荐引用方式 GB/T 7714 | Wei, Dasheng,Xu, Fei. Counting integral points in certain homogeneous spaces[J]. JOURNAL OF ALGEBRA,2016,448:350-398. |
| APA | Wei, Dasheng,&Xu, Fei.(2016).Counting integral points in certain homogeneous spaces.JOURNAL OF ALGEBRA,448,350-398. |
| MLA | Wei, Dasheng,et al."Counting integral points in certain homogeneous spaces".JOURNAL OF ALGEBRA 448(2016):350-398. |
入库方式： OAI收割
来源：数学与系统科学研究院
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