CM fields of Dihedral type and the Colmez conjecture
Yang, Tonghai1; Yin, Hongbo2
AbstractIn 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 '.
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000429343400001
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Document Type期刊论文
Corresponding AuthorYang, Tonghai
Affiliation1.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
Recommended Citation
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.
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