Counting integral points in certain homogeneous spaces

doi:10.1016/j.jalgebra.2015.09.043

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	Counting integral points in certain homogeneous spaces
	Wei, Dasheng1,2 ; Xu, Fei 3
刊名	JOURNAL OF ALGEBRA
	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
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000375634500011
内容类型	期刊论文
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.