共查询到20条相似文献,搜索用时 46 毫秒
1.
We obtain lower bound of caliber number of real quadratic field using splitting primes in K. We find all real quadratic fields of caliber number 1 and find all real quadratic fields of caliber number 2 if d is not 5 modulo 8. In both cases, we don't rely on the assumption on ζK(1/2). 相似文献
2.
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
3.
Frank Gerth III 《Journal of Number Theory》2006,118(1):90-97
Let K be a real quadratic field with 2-class rank equal to 4 or 5 and 4-class rank equal to 3. This paper computes density information for such fields to have infinite Hilbert 2-class field towers. 相似文献
4.
Stéphane R. Louboutin 《Journal of Number Theory》2009,129(10):2289-2294
J. Cohen, J. Sonn, F. Sairaiji and K. Shimizu proved that there are only finitely many imaginary quadratic number fields K whose Ono invariants OnoK are equal to their class numbers hK. Assuming a Restricted Riemann Hypothesis, namely that the Dedekind zeta functions of imaginary quadratic number fields K have no Siegel zeros, we determine all these K's. There are 114 such K's. We also prove that we are missing at most one such K. M. Ishibashi proved that if OnoK is large enough compared with hK, then the ideal class groups of K is cyclic. We give a short proof and a precision of Ishibashi's result. We prove that there are only finitely many imaginary quadratic number fields K satisfying Ishibashi's sufficient condition. Assuming our Restricted Riemann Hypothesis, we prove that the absolute values dK of their discriminants are less than 2.3⋅109. We determine all these K's with dK?106. There are 76 such K's. We prove that there is at most one such K with dK?1.8⋅1011. 相似文献
5.
A. Mouhib 《Journal of Number Theory》2009,129(6):1205-1211
This paper investigates the 2-class group of real multiquadratic number fields. Let p1,p2,…,pn be distinct primes and . We draw a list of all fields K whose 2-class group is trivial. 相似文献
6.
In this paper, we give parametric families of both real and complex quadratic number fields whose class group has 3-rank at least 2. As a consequence, we obtain that for all large positive real numbers x, the number of both real and complex quadratic fields whose class group has 3-rank at least 2 and absolute value of the discriminant ?x is >cx1/3, where c is some positive constant. 相似文献
7.
Sey Kim 《Journal of Number Theory》2006,121(1):7-29
Given any distinct prime numbers p,q, and r satisfying certain simple congruence conditions, we display a congruence relation between the fundamental units for the biquadratic field , modulo a certain prime ideal of OK. This congruence in particular implies the validity of the equivariant Tamagawa number conjecture formulated by Burns and Flach for the pair (h0(SpecK),Z[Gal(K/Q)]). 相似文献
8.
Artūras Dubickas 《Indagationes Mathematicae》2006,17(1):31-36
For a number field K, we give a complete characterization of algebraic numbers which can be expressed by a difference of two K-conjugate algebraic integers. These turn out to be the algebraic integers whose Galois group contains an element, acting as a cycle on some collection of conjugates which sum to zero. Hence there are no algebraic integers which can be written as a difference of two conjugate algebraic numbers but cannot be written as a difference of two conjugate algebraic integers. A generalization of the construction to a commutative ring is also given. Furthermore, we show that for n ?_ 3 there exist algebraic integers which can be written as a linear form in n K-conjugate algebraic numbers but cannot be written by the same linear form in K-conjugate algebraic integers. 相似文献
9.
David Vauclair 《Journal of Number Theory》2008,128(3):619-638
Following Kahn, and Assim and Movahhedi, we look for bounds for the order of the capitulation kernels of higher K-groups of S-integers into abelian S-ramified p-extensions. The basic strategy is to change twists inside some Galois-cohomology groups, which is done via the comparison of Tate Kernels of higher order. We investigate two ways: a global one, valid for twists close to 0 (in a certain sense), and a local one, valid for twists close to 1 in cyclic extensions. The global method produces lower bounds for abelian p-extensions which are S-ramified, but not Zp-embeddable. The local method is close to that of [J. Assim, A. Movahhedi, Bounds for étale capitulation kernels, K-Theory 33 (2004) 199-213], but is improved to take into consideration what happens when S consists of only the p-places. In contrast to the first one, one can expect this second method to produce nontrivial lower bounds in certain Zp-extensions. For example, we construct Zp-extensions in which the capitulation kernel is as big as we want (when letting the twist vary). We also include a complete solution to the problem of comparing Tate Kernels. 相似文献
10.
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
11.
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
12.
In this paper abelian function fields are restricted to the subfields of cyclotomic function fields. For any abelian function field K/k with conductor an irreducible polynomial over a finite field of odd characteristic, we give a calculating formula of the relative divisor class number of K. And using the given calculating formula we obtain a criterion for checking whether or not the relative divisor class number is divisible by the characteristic of k. 相似文献
13.
Suppose K is a field, αn∈K∗, and n is the least natural number with this property. We study the question on how many powers αj, 0?j<n, lie in a given K-linear space. 相似文献
14.
Let φ be a Drinfeld A-module of arbitrary rank and generic characteristic over a finitely generated field K. If the endomorphism ring of φ over an algebraic closure of K is equal to A, we prove that the image of the adelic Galois representation associated to φ is open. 相似文献
15.
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
16.
Franz Halter-Koch 《Journal of Pure and Applied Algebra》2007,209(3):763-770
Let R be an integral domain with quotient field K and L⊃K a finite extension field. By an R-lattice in L we mean a finitely generated R-module containing a basis of L over K. The set of all R-lattices is a commutative multiplicative semigroup. If R is one-dimensional and noetherian, we determine the structure of this semigroup and of the corresponding class semigroup by means of its partial Ponizovski factors. If moreover R is a Dedekind domain and L⊃K is separable, we give criteria for the partial Ponizovski factors to be groups in terms of the different and the conductor of their endomorphism rings. 相似文献
17.
Lenny Fukshansky 《Journal of Number Theory》2010,130(10):2099-2118
Text
Let K be a number field, , or the field of rational functions on a smooth projective curve over a perfect field, and let V be a subspace of KN, N?2. Let ZK be a union of varieties defined over K such that V?ZK. We prove the existence of a point of small height in V?ZK, providing an explicit upper bound on the height of such a point in terms of the height of V and the degree of a hypersurface containing ZK, where dependence on both is optimal. This generalizes and improves upon the results of Fukshansky (2006) [6] and [7]. As a part of our argument, we provide a basic extension of the function field version of Siegel's lemma (Thunder, 1995) [21] to an inequality with inhomogeneous heights. As a corollary of the method, we derive an explicit lower bound for the number of algebraic integers of bounded height in a fixed number field.Video
For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=R-o6lr8s0Go. 相似文献18.
Richard Pink 《Journal of Number Theory》2006,116(2):324-347
Let ? be a Drinfeld A-module of rank r over a finitely generated field K. Assume that ? has special characteristic p0 and consider any prime p≠p0 of A. If EndKsep(?)=A, we prove that the image of Gal(Ksep/K) in its representation on the p-adic Tate module of ? is Zariski dense in GLr. 相似文献
19.
Let φ be a Drinfeld A-module of arbitrary rank and arbitrary characteristic over a finitely generated field K, and set GK=Gal(Ksep/K). Let E=EndK(φ). We show that for almost all primes p of A the image of the group ring A[GK] in EndA(Tp(φ)) is the commutant of E. In the special case E=A it follows that the representation of GK on the p-torsion points φ[p](Ksep) of φ is absolutely irreducible for almost all p. 相似文献
20.
Xia Gao 《Journal of Number Theory》2011,131(6):994-1019