共查询到20条相似文献,搜索用时 15 毫秒
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Frank Gerth III 《manuscripta mathematica》1991,70(1):39-50
Letp be an odd prime number, and letK be a cyclic extension of ℚ(ζ) of degreep, where ζ is a primitivep-th root of unity. LetC
K
be thep-class group ofK, and letr
K
be the minimal number of generators ofC
K
1−σ
as a module over Gal(K/ℚ(ζ)), were σ is a generator of Gal(K/ℚ(ζ)). This paper shows how likely it is forr
K
= 0, 1, 2, … whenp=3, 5, or 7, and describes the obstacle to generalizing these results to regular primesp>7. 相似文献
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In this paper, we will calculate the number of Galois extensions of local fields with Galois group or .
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In this paper, we present some explicit formulas for the 3-rank of the tame kernels of certain pure cubic number fields, and give the density results concerning the 3-rank of the tame kernels. Numerical examples are given in Tables 1 and 2. 相似文献
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Periodica Mathematica Hungarica - Let $$pequiv -q equiv 5pmod 8$$ be two prime integers. In this paper, we investigate the unit groups of the fields $$ L_1 =mathbb {Q}(sqrt{2}, sqrt{p},... 相似文献
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We determine the isomorphism class of the Brauer groups of certain nonrational genus zero extensions of number fields. In particular, for all genus zero extensions of the rational numbers that are split by , .
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Let F be a cubic cyclic field with t(2)ramified primes.For a finite abelian group G,let r3(G)be the 3-rank of G.If 3 does not ramify in F,then it is proved that t-1 r3(K2O F)2t.Furthermore,if t is fixed,for any s satisfying t-1 s 2t-1,there is always a cubic cyclic field F with exactly t ramified primes such that r3(K2O F)=s.It is also proved that the densities for 3-ranks of tame kernels of cyclic cubic number fields satisfy a Cohen-Lenstra type formula d∞,r=3-r2∞k=1(1-3-k)r k=1(1-3-k)2.This suggests that the Cohen-Lenstra conjecture for ideal class groups can be extended to the tame kernels of cyclic cubic number fields. 相似文献
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Cohomology groups Hs(Zn,Zm) are studied to describe all groups up to isomorphism which are (central) extensions of the cyclic group Zn by the Zn-module Zm. Further, for each such a group the number of non-equivalent extensions is determined. 相似文献
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J. E. Carter 《Archiv der Mathematik》2003,81(3):266-271
Let K be a number field and let G be a finite abelian group. We call
K a Hilbert-Speiser field of type G if, and only if, every tamely
ramified normal extension L/K with Galois group isomorphic to G has
a normal integral basis. Now let C2 and C3 denote the cyclic
groups of order 2 and 3, respectively. Firstly, we show that among all
imaginary quadratic fields, there are exactly three Hilbert-Speiser
fields of type $C_{2}: \mathbb{Q}(\sqrt {m})$, where $m \in \{-1, -3, -7\}$.
Secondly, we give some necessary and sufficient conditions for a real
quadratic field $K = \mathbb{Q}(\sqrt {m})$ to be a Hilbert-Speiser field of
type C2. These conditions are in terms of the congruence class of m
modulo 4 or 8, the fundamental unit of K, and the class number of K.
Finally, we show that among all quadratic number fields, there are
exactly eight Hilbert-Speiser fields of type $C_{3}: \mathbb{Q}(\sqrt {m})$,
where $m \in \{-11,-3, -2, 2, 5, 17, 41, 89\}$.Received: 2 April 2002 相似文献
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Robert Laterveer 《数学学报(英文版)》2017,33(7):887-898
This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold X in the family has an involution such that the induced involution on the Fano variety F of lines in X is symplectic and has a K3 surface S in the fixed locus. The main result establishes a relation between X and S on the level of Chow motives. As a consequence, we can prove finite-dimensionality of the motive of certain members of the family. 相似文献
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Aouissi S. Mayer D. C. Ismaili M. C. Talbi M. Azizi A. 《Periodica Mathematica Hungarica》2020,81(2):250-274
Periodica Mathematica Hungarica - Let $$k=k_0(\root 3 \of {d})$$ be a cubic Kummer extension of $$k_0=\mathbb {Q}(\zeta _3)$$ with $$d>1$$ a cube-free integer and $$\zeta _3$$ a primitive... 相似文献
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Frank Gerth III 《Proceedings of the American Mathematical Society》2001,129(9):2547-2552
Let be a square-free positive integer. Let denote the 4-class rank of a quadratic field . This paper examines how likely it is for and for .
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Elliot Benjamin 《The Ramanujan Journal》2006,11(1):103-110
Let
be an imaginary biquadratic number field with Clk,2, the 2-class group of k, isomorphic to Z/2Z × Z/2mZ, m > 1, with q a prime congruent to 3 mod 4 and d a square-free positive integer relatively prime to q. For a number of fields k of the above type we determine if the 2-class field tower of k has length greater than or equal to 2. To establish these results we utilize capitulation of ideal classes in the three unramified
quadratic extensions of k, ambiguous class number formulas, results concerning the fundamental units of real biquadratic number fields, and criteria
for imaginary quadratic number fields to have 2-class field tower length 1.
2000 Mathematics Subject Classification Primary—11R29 相似文献
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Wolfgang Müller 《Monatshefte für Mathematik》1988,106(3):211-219
LetK be a cubic number field. Denote byA K (x) the number of ideals with ideal norm ≤x, and byQ K (x) the corresponding number of squarefree ideals. The following asymptotics are proved. For every ε>0 ε>0 $$\begin{gathered} {\text{ }}A_K (x) = c_1 x + O(x^{43/96 + \in } ), \hfill \\ Q_K (x) = c_2 x + O(x^{1/2} \exp {\text{ }}\{ - c(\log {\text{ }}x)^{3/5} (\log \log {\text{ }}x)^{ - 1/5} \} ). \hfill \\ \end{gathered}$$ Herec 1,c 2 andc are positive constants. Assuming the Riemann hypotheses for the Dedekind zeta function ζ K , the error term in the second result can be improved toO(x 53/116+ε). 相似文献
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Dongho Byeon 《Proceedings of the American Mathematical Society》2000,128(5):1319-1323
We give some necessary conditions for class numbers of the simplest cubic fields to be 3 and, using Lettl's lower bounds of residues at of Dedekind zeta functions attached to cyclic cubic fields, determine all the simplest cubic fields of class number 3.