KMS Of Academy of mathematics and systems sciences, CAS
| The Lambda Invariants at CM Points | |
| Yang, Tonghai1; Yin, Hongbo2; Yu, Peng3 | |
| 2021-04-01 | |
| 发表期刊 | INTERNATIONAL MATHEMATICS RESEARCH NOTICES
 |
| ISSN | 1073-7928 |
| 卷号 | 2021期号:7页码:5542-5603 |
| 摘要 | In this paper, we show that lambda(z(1)) - lambda(z(2)), lambda(z(1)), and 1 - lambda(z(1)) are all Borcherds products on X(2) x X(2). We then use the big CM value formula of Bruinier, Kudla, and Yang to give explicit factorization formulas for the norms of lambda( d +root d/2), 1 - lambda(d+root d/2), and lambda( d(1) +root d(1)/2) - lambda(d(2)+root d(2)/2), with the latter under the condition (d(1), d(2)) = 1. Finally, we use these results to show that lambda( d +root d/2) is always an algebraic integer and can be easily used to construct units in the ray class field of Q(root d) of modulus 2. In the process, we also give explicit formulas for a whole family of local Whittaker functions, which are of independent interest. |
| DOI | 10.1093/imrn/rnz230 |
| 收录类别 | SCI |
| 语种 | 英语 |
| 资助项目 | NSF[DMS-1762289] ; NSFC[NSFC-11701548] ; Young Scholars Program of Shandong University |
| WOS研究方向 | Mathematics |
| WOS类目 | Mathematics |
| WOS记录号 | WOS:000648945900023 |
| 出版者 | OXFORD UNIV 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/58729 |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Yang, Tonghai |
| 作者单位 | 1.Univ Wisconsin Madison, Dept Math, Van Vleck Hall, Madison, WI 53706 USA 2.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Yang, Tonghai,Yin, Hongbo,Yu, Peng. The Lambda Invariants at CM Points[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES,2021,2021(7):5542-5603. |
| APA | Yang, Tonghai,Yin, Hongbo,&Yu, Peng.(2021).The Lambda Invariants at CM Points.INTERNATIONAL MATHEMATICS RESEARCH NOTICES,2021(7),5542-5603. |
| MLA | Yang, Tonghai,et al."The Lambda Invariants at CM Points".INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2021.7(2021):5542-5603. |
| 条目包含的文件 | 条目无相关文件。 | |||||
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。
修改评论