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The Lambda Invariants at CM Points

文献类型：期刊论文

作者Yang, Tonghai3; Yin, Hongbo2; Yu, Peng1
刊名INTERNATIONAL MATHEMATICS RESEARCH NOTICES
出版日期2021-04-01
卷号2021期号:7页码:5542-5603
ISSN号1073-7928
DOI10.1093/imrn/rnz230
英文摘要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.
资助项目NSF[DMS-1762289] ; NSFC[NSFC-11701548] ; Young Scholars Program of Shandong University
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000648945900023
出版者OXFORD UNIV PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58728]  
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.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China
2.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
3.Univ Wisconsin Madison, Dept Math, Van Vleck Hall, Madison, WI 53706 USA
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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