Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: CM fields of Dyhedral type and the Colmez conjecture   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 $\Q$ (cyclotomic characters). In this
paper, we also prove that the Colmez conjecture holds for `unitary CM types of
signature $(n-1, 1)$' and holds on average for `unitary CM types of a fixed CM
number field of signature $(n-r, r)$'.

30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin