共查询到20条相似文献,搜索用时 542 毫秒
1.
Ichiro Miyada 《manuscripta mathematica》1995,88(1):535-540
We show that there exist only finitely many imaginary abelian number fields of type (2,2,...,2) with one class in each genus.
Moreover, if the Generalized Riemann Hypothesis is true, we have exactly 301 such fields, whose degrees are less than or equal
to 23. Finally we give the table of those 301 fields. 相似文献
2.
Let K be an imaginary abelian number field. We determine the unit index of K of certain type whose conductor is a product of two or three prime powers. As a consequence we construct some counterexamples to Satz 29 in Hasse's monograph [2]. 相似文献
3.
In their 1934 paper, Scholz and Taussky defined the notion of capitulation type for imaginary quadratic fields whose ideal class group has a Sylow 3-subgroup which is elementary abelian of order 32. For one particular capitulation type (type D) they prove that the 3-class field tower of the quadratic field has length 2. They briefly indicate how a similar result can be shown to hold for capitulation type E. In this paper we give a simpler proof of their type D result and we construct a group theoretic counterexample to their type E assertion. 相似文献
4.
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
5.
Friedrich Sauvigny 《manuscripta mathematica》1992,74(1):83-86
The aim of this paper is to give a new proof of the gradient estimate for graphs of prescribed mean curvatureH=H(x,y,z). Similarly as in [2] where the caseH=H(x,y) is studied, we introduce conformal parameters for the surface. Then we employ the differential equation for the unit normal
of the surface derived in [3] Satz 1. By this method, which is contained in [4] Satz 4, we prove the following 相似文献
6.
We characterize those imaginary quadratic number fields, k, with 2-class group of type (2,2,2) and with the 2-rank of the class group of its Hilbert 2-class field equal to 2. We then compute the length of the 2-class field tower of k. 相似文献
7.
Franz Lemmermeyer 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):335-345
In a series of articles published in the C.R. Paris more than a century ago, T. PéPIN announced a list of “theorems” concerning
the solvability of diophantine equations of the type ax4 +by
4 = z2. In this article, we show how to prove these claims using the structure of 2-class groups of imaginary quadratic number fields.
We will also look at a few related results from a modern point of view. 相似文献
8.
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
9.
Norio Adachi 《Journal of Number Theory》1973,5(4):253-265
We give a necessary and sufficient condition for the relative class number of an imaginary field contained in Q(e2πi/p?) to be divisible by p. We also give a sufficient condition for the class number of a real field contained in Q(e2πi/p?) not to be divisible by p. 相似文献
10.
F. Lemmermeyer 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1997,67(1):205-214
We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2, 2, 2) whose Hilbert 2-class fields are finite. 相似文献
11.
We deal with the well-known operation ofARTIN?S Braid GroupB n on the free groupF n by automorphisms, and give a proof for a theorem ofBIRMAN/HILDEN (here Satz B) by showing, that the images of the generators ofF n underB n are of a special form (Satz C). The theory ofBRIESKORN?S Automorphic Sets comes in here. With similar methods we give a proof of a theorem of Magnus saying thatB n operates on a certain polynomial ring effectively by automorphisms (here Satz 9.2). 相似文献
12.
We prove a ‘minimal’ type automorphy lifting theorem for 2-adic Galois representations of unitary type, over imaginary CM fields. We use this to improve an automorphy lifting theorem of Kisin for \({{\mathrm{GL}}}_2\). 相似文献
13.
We illustrate the connection between homogeneous perturbations of homogeneous Gaussian random fields over Rn or Zn, with values in Rm, and classical as well as quantum statistical mechanics. In particular we construct homogeneous non-Gaussian random fields as weak limits of perturbed Gaussian random fields and study the infinite volume limit of correlation functions for a classical continuous gas of particles with inner degrees of freedom. We also exhibit the relation between quantum statistical mechanics of lattice systems (anharmonic crystals) at temperature β?1 and homogeneous random fields over Zn × Sβ, where Sβ is the circle of length β, which then provides a connection also with classical statistical mechanics. We obtain the infinite volume limit of real and imaginary times Green's functions and establish its properties. We also give similar results for the Gibbs state of the correspondent classical lattice systems and show that it is the limit as h → 0 of the quantum statistical Gibbs state. 相似文献
14.
H. K. Pathak A. S. Grewal 《International Journal of Mathematical Education in Science & Technology》2013,44(4):575-583
A general cubic equation ax 3 + bx 2 + cx + d = 0 where a, b, c, d ∈R, a ≠ 0 has three roots with two possibilities—either all three roots are real or one root is real and the remaining two roots are imaginary. Dealing with the second possibility this paper attempts to give the geometrical locations of the imaginary roots of the equation under three different sets of conditions. These sets of conditions include: (i) the real root of the given cubic equation is given, (ii) the real part of an imaginary root is given, and (iii) the imaginary part of an imaginary root is given. 相似文献
15.
Stphane Louboutin 《Mathematische Nachrichten》1997,183(1):173-184
We give a necessary condition for the ideal class group of a CM-field to be of exponent at most two. This condition enables us to drastically reduce the amount of relative class number computation for determination of the CM - fields of some types (e. g. the imaginary cyclic non -quadratic number fields of 2 - power degrees) whose ideal class groups are of exponents at most two. We also give a necessary condition for some quartic non - CM - fields to have class number one. 相似文献
16.
In this article, we prove that an imaginary quadratic field F has the ideal class group isomorphic to ?/2? ⊕ ?/2? if and only if the Ono number of F is 3 and F has exactly 3 ramified primes under the Extended Riemann Hypothesis (ERH). In addition, we give the list of all imaginary quadratic fields with Ono number 3. 相似文献
17.
M. M. Malamud 《Journal of Mathematical Sciences》2003,115(2):2199-2222
We give sufficient conditions under which the non-self-adjoint operator A = G + iV
1/2
JV
1/2 (with a well-defined imaginary part) is similar to a self-adjoint one. We also give sufficient conditions (these conditions become necessary in the dissipative case) under which the triangular operator
is similar to a self-adjoint one. Bibliography: 34 titles. 相似文献
18.
The minimal polynomials of the singular values of the classical Weber modular functions give far simpler defining polynomials for the class fields of imaginary quadratic fields than the minimal polynomials of singular moduli of level 1. We describe computations of these polynomials and give conjectural formulas describing the prime decomposition of their resultants and discriminants, extending the formulas of Gross-Zagier for the level 1 case.
19.
《Journal of Number Theory》1986,24(1):7-19
The goals of this paper are to provide: (1) sufficient conditions, based on the solvability of certain diophantine equations, for the non-triviality of the class numbers of certain real quadratic fields; (2) sufficient conditions for the divisibility of the class numbers of certain imaginary quadratic fields by a given integer; and (3) necessary and sufficient conditions for an algebraic integer (which is not a unit) to be the norm of an algebraic integer in a given extension of number fields. 相似文献
20.
We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c1(2,2)in terms of the indices of the bundles,and extend the result to arbitrary higher rank case.We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability. 相似文献