Grunwald-Wang theorem, an effective version
文献类型：期刊论文
| 作者 | Wang Song1,2
|
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2015-08-01 |
| 卷号 | 58期号:8页码:1589-1606 |
| 关键词 | Grunwald-Wang theorem class field theory bound |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-015-4977-5 |
| 英文摘要 | 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l (r) | phi(N) and p is not an l-th power mod N. Some part of this article is adopted (with some revision) from the unpublished thesis by Wang (2001). |
| 语种 | 英语 |
| WOS记录号 | WOS:000358172300001 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/20381]  |
| 专题 | 数学所 |
| 通讯作者 | Wang Song |
| 作者单位 | 1.Chinese Acad Sci, HUA Loo Keng Key Lab Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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