Grunwald-Wang theorem, an effective version

doi:10.1007/s11425-015-4977-5

CSpace > 数学所

	Grunwald-Wang theorem, an effective version
	Wang Song1,2
	2015-08-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	58 期号:8 页码:1589-1606
摘要	The main purpose of this article is to establish an effective version of the Grunwald-Wang theorem, which asserts that given a family of local characters chi (v) of K (v) * of exponent m, where v A1/4 S for a finite set S of primes of K, there exists a global character chi of the idele class group C (K) of exponent m (unless some special case occurs, when it is 2m) whose local component at v is chi (v) . The effectiveness problem for this theorem is to bound the norm N(chi) of the conductor of chi in terms of K, m, S and N(chi (v) ) (v a S). The Kummer case (when K contains mu (m) ) is easy since it is almost an application of the Chinese remainder theorem. In this paper, we solve this problem completely in general case, and give three versions of bound, one is with GRH, and the other two are unconditional bounds. These effective results have some interesting applications in concrete situations. To give a simple example, if we fix p and l, one gets a good least upper bound for N such that p is not an l-th power mod N. One also gets the least upper bound for N such that l (r) \| phi(N) and p is not an l-th power mod N. Some part of this article is adopted (with some revision) from the unpublished thesis by Wang (2001).
关键词	Grunwald-Wang theorem class field theory bound
DOI	10.1007/s11425-015-4977-5
语种	英语
资助项目	National Basic Research Program of China (973 Program)[2013CB834202] ; National Natural Science Foundation of China[11321101] ; One Hundred Talent's Program from Chinese Academy of Sciences
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000358172300001
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20382
专题	数学所
通讯作者	Wang Song
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, HUA Loo Keng Key Lab Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang Song. Grunwald-Wang theorem, an effective version[J]. SCIENCE CHINA-MATHEMATICS,2015,58(8):1589-1606.
APA	Wang Song.(2015).Grunwald-Wang theorem, an effective version.SCIENCE CHINA-MATHEMATICS,58(8),1589-1606.
MLA	Wang Song."Grunwald-Wang theorem, an effective version".SCIENCE CHINA-MATHEMATICS 58.8(2015):1589-1606.