共查询到20条相似文献,搜索用时 15 毫秒
1.
Ali Mouhib 《Mathematische Nachrichten》2016,289(14-15):1927-1933
We study the capitulation problem of the 2‐class group of some cyclic number fields M with large degree and 2‐class group isomorphic to . Precisely, we give the structure of the Galois group of the maximal unramified 2‐extension over M. 相似文献
2.
Let p be a prime number. In [15], we studied the class semigroup of the ring of integers of the cyclotomic -extension of the rationals. In this paper, we generalize the result to some -extensions of number fields. Moreover, we investigate the relation between the class semigroup and Iwasawa invariants. 相似文献
3.
This paper shows that a positive proportion of the imaginary quadratic
fields with 2-class rank equal to 3 have 4-class rank equal to zero and
infinite Hilbert 2-class field towers.
Received: 14 January 2003 相似文献
4.
Yutaka Konomi 《Journal of Number Theory》2011,131(6):1062-1069
We study the relation between the minus part of the p-class subgroup of a dihedral extension over an imaginary quadratic field and the special value of the Artin L-function at 0. 相似文献
5.
The difference between the 3-rank of the ideal class group
of an imaginary quadratic field
and that of the associated real quadratic field
is equal to 0 or 1. In this note, we give an infinite family of
examples in each case.Received: 9 September 2002 相似文献
6.
Fix a totally real number field F of degree at least 2. Under the assumptions of the generalized Riemann hypothesis and Artin's conjecture on the entirety of Artin L-functions, we derive an upper bound (in terms of the discriminant) on the class number of any CM number field with maximal real subfield F. This bound is a refinement of a bound established by Duke in 2001. Under the same hypotheses, we go on to prove that there exist infinitely many CM-extensions of F whose class numbers essentially meet this improved bound and whose Galois groups are as large as possible. 相似文献
7.
Let F be a cubic cyclic field with exactly one ramified prime p,p>7, or , a real quadratic field with . In this paper, we study the 3-primary part of K2OF. If 3 does not divide the class number of F, we get some results about the 9-rank of K2OF. In particular, in the case of a cubic cyclic field F with only one ramified prime p>7, we prove that four conclusions concerning the 3-primary part of K2OF, obtained by J. Browkin by numerical computations for primes p, 7≤p≤5000, are true in general. 相似文献
8.
We establish the fundamental results of genus theory for finite (non necessary Galois) extensions of global fields by using
narrow S-class groups, when S is an arbitrary finite set of places. This exposition, which involves both the number fields and the functions fields cases,
generalizes most classical results on this subject.
Received: 8 February 1999 / Revised version: 17 December 1999 相似文献
9.
Cristian D. Popescu 《Journal of Number Theory》2005,115(1):27-44
We show that, for all characteristic p global fields k and natural numbers n coprime to the order of the non-p-part of the Picard group Pic0(k) of k, there exists an abelian extension L/k whose local degree at every prime of k is equal to n. This answers in the affirmative in this context a question recently posed by Kisilevsky and Sonn. As a consequence, we show that, for all n and k as above, the n-torsion subgroup Brn(k) of the Brauer group Br(k) of k is algebraic, answering a question of Aldjaeff and Sonn in this context. 相似文献
10.
Soogil Seo 《manuscripta mathematica》2008,127(3):381-396
A circular distribution is a Galois equivariant map ψ from the roots of unity μ
∞ to an algebraic closure of such that ψ satisfies product conditions, for ϵ ∈ μ
∞ and , and congruence conditions for each prime number l and with (l, s) = 1, modulo primes over l for all , where μ
l
and μ
s
denote respectively the sets of lth and sth roots of unity. For such ψ, let be the group generated over by and let be , where U
s
denotes the global units of . We give formulas for the indices and of and inside the circular numbers P
s
and units C
s
of Sinnott over .
This work was supported by the SRC Program of Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government
(MOST) (No. R11-2007-035-01001-0). This work was supported by the Korea Research Foundation Grant funded by the Korean Government
(MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00455). 相似文献
11.
Let a cyclic group $G$ act either on a number field $\mathbb L$
or on a $3$-manifold $M$. Let $s_{\mathbb L}$ be the number of
ramified primes in the extension $\mathbb L^G\subset \mathbb L$ and $s_M$ be the number
of components of the branching set of the branched covering
$M\to M/G$. In this paper, we prove several formulas relating
$s_{\mathbb L}$ and $s_M$ to the induced $G$-action on $Cl(\mathbb L)$ and
$H_1(M),$ respectively.
We observe that the formulas for $3$-manifolds and number fields are
almost identical, and therefore, they provide new evidence for
the correspondence between $3$-manifolds and number fields
postulated in arithmetic topology. 相似文献
12.
O. Sauzet 《manuscripta mathematica》1998,96(3):263-273
We study Iwasawa theory for p-rational and p-birational fields. A classical invariant characterises them and, in the case of CM-fields, this gives an explicit characterisation.
We show how to compute those fields and and give numerical examples for small degrees.
Received: 20 May 1997 / Revised version: 9 April 1998 相似文献
13.
Masato Kurihara 《Journal of the European Mathematical Society》1999,1(1):35-49
In this paper, for a totally real number field k we show the ideal class group of k(∪n>0μn)+ is trivial. We also study the p-component of the ideal class group of the cyclotomic Zp-extension.
Received January 15, 1998 / final version received July 31, 1998 相似文献
14.
The purpose of this paper is to exhibit a new family of real bicyclic biquadratic fields K for which we can write the Hasse unit index of the group generated by the units of the three quadratic subfields in the unit group E K of K. As a byproduct, one can explicitly relate the class number of K with the product of the class numbers of the three quadratic subfields. Received: 25 July 2000 / Revised version: 12 December 2000 相似文献
15.
For an algebraic number field k and a prime number p (if p=2, we assume that μ4⊂k), we study the maximal rank ρ
p
of a free pro-p-extension of k. This problem is related to deep conjectures of Greenberg in Iwasawa theory. We give different equivalent formulations of
these conjectures and we apply them to show that, essentially, ρ
k
=r
2(k)+1 if and only if k is a so-called p-rational field.
Received: 29 April 1999 / Revised version: 31 January 2000 相似文献
16.
We answer a question of M. Flach by showing that there is a linear representation of a profinite group whose (unrestricted)
universal deformation ring is not a complete intersection. We show that such examples arise in arithmetic in the following
way. There are infinitely many real quadratic fields F for which there is a mod 2 representation of the Galois group of the maximal unramified extension of F whose universal deformation ring is not a complete intersection. Finally, we discuss bounds on the singularities of universal
deformation rings of representations of finite groups in terms of the nilpotency of the associated defect groups.
The first author was supported in part by NSF Grant DMS01-39737 and NSA Grant H98230-06-1-0021. The second author was supported
in part by NSF Grants DMS00-70433 and DMS05-00106. 相似文献
17.
We prove that the submodule in K-theory which gives the exact value
of the L-function by the Beilinson regulator map at non-critical values for Hecke characters of imaginary quadratic fields K with cl (K) = 1(p-local Tamagawa number conjecture) satisfies that the length of its coimage under the local Soulé regulator map is the p-adic valuation of certain special values of p-adic L-functions associated to the Hecke characters. This result yields immediately, up to Jannsens conjecture, an upper bound for
in terms of the valuation of these p-adic L-functions, where Vp denotes the p-adic realization of a Hecke motive.Received: 4 June 2003 相似文献
18.
Andrew Sale 《代数通讯》2013,41(2):873-897
Determining the length of short conjugators in a group can be considered as an effective version of the conjugacy problem. The conjugacy length function provides a measure for these lengths. We study the behavior of conjugacy length functions under group extensions, introducing the twisted and restricted conjugacy length functions. We apply these results to show that certain abelian-by-cyclic groups have linear conjugacy length function and certain semidirect products ?d ? ?k have at most exponential (if k > 1) or linear (if k = 1) conjugacy length functions. 相似文献
19.
F. Lemmermeyer 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2006,76(1):279-293
In this article we study the 2-Selmer groups of number fieldsF as well as some related groups, and present connections to the quadratic reciprocity law inF. 相似文献
20.
《Expositiones Mathematicae》2022,40(3):665-678
In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asymptotic formula for the number of representations of an integer in this form. The result is deeply related with the divisor function. In the course of our study we get an independent result about it. Concretely we are able to deduce a new upper bound for the divisor function fully explicit. 相似文献