The Lambda Invariants at CM Points

doi:10.1093/imrn/rnz230

	The Lambda Invariants at CM Points
	Yang, Tonghai 3; Yin, Hongbo 2; Yu, Peng 1
刊名	INTERNATIONAL MATHEMATICS RESEARCH NOTICES
	2021-04-01
卷号	2021 期号:7 页码:5542-5603
ISSN号	1073-7928
DOI	10.1093/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
出版者	OXFORD UNIV PRESS
WOS记录号	WOS:000648945900023
内容类型	期刊论文
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.