Counting integral points in certain homogeneous spaces

doi:10.1016/j.jalgebra.2015.09.043

CSpace > 数学所

	Counting integral points in certain homogeneous spaces
	Wei, Dasheng1,2 ; Xu, Fei 3
	2016-02-15
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	448 页码:350-398
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.
关键词	Integral point Homogeneous space Tamagawa measure
DOI	10.1016/j.jalgebra.2015.09.043
语种	英语
资助项目	NSFC[10671104] ; NSFC[11031004] ; 973 Program[2013CB834202] ; Deutsche Forschungsgemeinschaft[DE 1646/2-1]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000375634500011
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22645
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.