CM fields of Dihedral type and the Colmez conjecture

doi:10.1007/s00229-017-0966-z

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	CM fields of Dihedral type and the Colmez conjecture
	Yang, Tonghai 1; Yin, Hongbo 2
	2018-05-01
发表期刊	MANUSCRIPTA MATHEMATICA
ISSN	0025-2611
卷号	156 期号:1-2 页码:1-22
摘要	In this paper, we consider some CM fields which we call of dihedral type and compute the Artin L-functions associated to all CM types of these CM fields. As a consequence of this calculation, we see that the Colmez conjecture in this case is very closely related to understanding the log derivatives of certain Hecke characters of real quadratic fields. Recall that the 'abelian case' of the Colmez conjecture, proved by Colmez himself, amounts to understanding the log derivatives of Hecke characters of (cyclotomic characters). In this paper, we also prove that the Colmez conjecture holds for 'unitary CM types of signature ' and holds on average for 'unitary CM types of a fixed CM number field of signature '.
DOI	10.1007/s00229-017-0966-z
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000429343400001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30080
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.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. CM fields of Dihedral type and the Colmez conjecture[J]. MANUSCRIPTA MATHEMATICA,2018,156(1-2):1-22.
APA	Yang, Tonghai,&Yin, Hongbo.(2018).CM fields of Dihedral type and the Colmez conjecture.MANUSCRIPTA MATHEMATICA,156(1-2),1-22.
MLA	Yang, Tonghai,et al."CM fields of Dihedral type and the Colmez conjecture".MANUSCRIPTA MATHEMATICA 156.1-2(2018):1-22.