共查询到20条相似文献,搜索用时 15 毫秒
1.
Haiyan Zhou 《代数通讯》2013,41(9):2810-2819
For any odd prime p, we prove some results connecting the p2-rank of the tame kernel of a quadratic field F with the p2-rank Cl(𝒪E1 ), where E1 is the maximal real subfield of F(ζp2 ). 相似文献
2.
Akinari Hoshi 《Journal of Number Theory》2011,131(11):2135-2150
Let m?−1 be an integer. We give a correspondence between integer solutions to the parametric family of cubic Thue equations
X3−mX2Y−(m+3)XY2−Y3=λ 相似文献
3.
András Vasy 《Advances in Mathematics》2010,223(1):49-97
In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds (X○,g) which are de Sitter-like at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces. Under global assumptions on the (null)bicharacteristic flow, namely that the boundary of the compactification X is a union of two disjoint manifolds, Y±, and each bicharacteristic converges to one of these two manifolds as the parameter along the bicharacteristic goes to +∞, and to the other manifold as the parameter goes to −∞, we also define the scattering operator, and show that it is a Fourier integral operator associated to the bicharacteristic flow from Y+ to Y−. 相似文献
4.
Thom Mulders 《K-Theory》1991,5(5):449-470
For many number fieldsF, it is proved that the tame kernel, K2(
), and the wild kernel, W(F), ofF are generated by Dennis-Stein symbols. For some real quadratic number fields, generators for the tame kernel are given. 相似文献
5.
Volker Ziegler 《Journal of Number Theory》2006,120(2):303-325
We consider the relative Thue inequalities
|X4−t2X2Y2+s2Y4|?2|t|−2|s|−2, 相似文献
6.
Manuel González 《Archiv der Mathematik》2011,97(4):345-352
The perturbation classes problem for semi-Fredholm operators asks when the equalities SS(X,Y)=PF+(X,Y){\mathcal{SS}(X,Y)=P\Phi_+(X,Y)} and SC(X,Y)=PF-(X,Y){\mathcal{SC}(X,Y)=P\Phi_-(X,Y)} are satisfied, where SS{\mathcal{SS}} and SC{\mathcal{SC}} denote the strictly singular and the strictly cosingular operators, and PΦ+ and PΦ− denote the perturbation classes for upper semi-Fredholm and lower semi-Fredholm operators. We show that, when Y is a reflexive Banach space, SS(Y*,X*)=PF+(Y*,X*){\mathcal{SS}(Y^*,X^*)=P\Phi_+(Y^*,X^*)} if and only if SC(X,Y)=PF-(X,Y),{\mathcal{SC}(X,Y)=P\Phi_-(X,Y),} and SC(Y*,X*)=PF-(Y*,X*){\mathcal{SC}(Y^*,X^*)=P\Phi_-(Y^*,X^*)} if and only if SS(X,Y)=PF+(X,Y){\mathcal{SS}(X,Y)=P\Phi_+(X,Y)}. Moreover we give examples showing that both direct implications fail in general. 相似文献
7.
We show that a maximal curve over Fq2 given by an equation A(X)=F(Y), where A(X)∈Fq2[X] is additive and separable and where F(Y)∈Fq2[Y] has degree m prime to the characteristic p, is such that all roots of A(X) belong to Fq2. In the particular case where F(Y)=Ym, we show that the degree m is a divisor of q+1. 相似文献
8.
Let E/F be a Galois extension of number fields with the quaternion Galois group Q 8. In this paper, we prove some relations connecting orders of the odd part of the kernel of the transfer map of the tame kernel of E with the same orders of some of its subfields. Let E/? be a Galois extension of number fields with the Galois group Q 8 and p an odd prime such that p ≡ 3 (mod 4). We prove that if there is at most one quadratic subfield such that the p-Sylow subgroup of the tame kernel is nontrivial, then p r -rank(K 2(E/K)) is even, i.e., 2|p r -rank(K 2(𝒪 E )) ? p r -rank(K 2(𝒪 K )), where K is the quartic subfield of E. 相似文献
9.
Suppose that p(X, Y) = A − BX − X(∗)B(∗) − CYC(∗) and q(X, Y) = A − BX + X(∗)B(∗) − CYC(∗) are quaternion matrix expressions, where A is persymmetric or perskew-symmetric. We in this paper derive the minimal rank formula of p(X, Y) with respect to pair of matrices X and Y = Y(∗), and the minimal rank formula of q(X, Y) with respect to pair of matrices X and Y = −Y(∗). As applications, we establish some necessary and sufficient conditions for the existence of the general (persymmetric or perskew-symmetric) solutions to some well-known linear quaternion matrix equations. The expressions are also given for the corresponding general solutions of the matrix equations when the solvability conditions are satisfied. At the same time, some useful consequences are also developed. 相似文献
10.
Alexander F. BrownEknath P. Ghate 《Journal of Number Theory》2002,95(1):14-37
We show that for a real quadratic field F the dihedral congruence primes with respect to F for cusp forms of weight k and quadratic nebentypus are essentially the primes dividing expressions of the form εk−1+±1 where ε+ is a totally positive fundamental unit of F. This extends work of Hida. Our results allows us to identify a family of (ray) class fields of F which are generated by torsion points on modular abelian varieties. 相似文献
11.
Let R be a discrete complete valuation ring, with field of fractions K, and with algebraically closed residue field k of characteristic p > 0. Let X be a germ of an R-curve at an ordinary double point. Consider a finite Galois covering f: Y → X, whose Galois group G is a p-group, such that Y is normal, and which is étale above Xk≔ x × rk. Asume that Y has a semi-stable model :→ Y over R, and let y be a closed point of Y. If the inertia subgroup I(y) at y is cyclic of order pn, we compute the p-rank of tf−1 (y) by using a result of Raynaud. In particular, we prove that this p-rank is bounded by pn −1. 相似文献
12.
Hai Yan ZHOU 《数学学报(英文版)》2007,23(10):1807-1812
It is well known that there is a close connection between tame kernels and ideal class groups of number fields. However, the latter is a very difficult subject in number theory. In this paper, we prove some results connecting the p^n-rank of the tame kernel of a cyclic cubic field F with the p^n-rank of the coinvariants of μp^n×CI(δE,T) under the action of the Galois group, where E = F(ζp^n ) and T is the finite set of primes of E consisting of the infinite primes and the finite primes dividing p. In particular, if F is a cyclic cubic field with only one ramified prime and p = 3, n = 2, we apply the results of the tame kernels to prove some results of the ideal class groups of E, the maximal real subfield of E and F(ζ3). 相似文献
13.
JinRong Wang 《Communications in Nonlinear Science & Numerical Simulation》2012,17(2):545-554
In this paper, existence and attractiveness of solutions for quadratic Urysohn fractional integral equations on an unbounded interval are obtained by virtue of Tichonov fixed point theorem and suitable conjunction of the well known measure ω0(X) and the spaces C(R+). Further, three certain solutions sets XL,γ, X1,α and X1,(1−(α+v)), which tending to zero at an appropriate rate t−ν (ν > 0), ν = γ (or α or 1 − (α + v)) as t → ∞, are introduced and stability of solutions for quadratic Urysohn fractional integral equations are obtained based on these solutions sets respectively by applying Schauder fixed point theorem via some easy checked conditions. An example is given to illustrate the results. 相似文献
14.
Sooraj Kuttykrishnan 《Journal of Pure and Applied Algebra》2009,213(1):127-135
We study the structure of length three polynomial automorphisms of R[X,Y] when R is a UFD. These results are used to prove that if SLm(R[X1,X2,…,Xn])=Em(R[X1,X2,…,Xn]) for all n≥0 and for all m≥3 then all length three polynomial automorphisms of R[X,Y] are stably tame. 相似文献
15.
《Journal of Pure and Applied Algebra》1996,106(1):103-112
A polynomial map F: R2 → R2 is said to satisfy the Jacobian condition if ∀(X, Y)ϵ R2, J(F)(X, Y) ≠ 0. The real Jacobian conjecture was the assertion that such a map is a global diffeomorphism. Recently the conjecture was shown to be false by S. Pinchuk. According to a theorem of J. Hadamard any counterexample to the conjecture must have asymptotic values. We give the structure of the variety of all the asymptotic values of a polynomial map F: R2 → R2 that satisfies the Jacobian condition. We prove that the study of the asymptotic values of such maps can be reduced to those maps that have only X- or Y-finite asymptotic values. We prove that a Y-finite asymptotic value can be realized by F along a rational curve of the type (X− k, A0 + A1 X + … + AN − 1 XN − 1 + YXN), where X → 0, Y is fixed and K, N > 0 are integers. More precisely we prove that the coordinate polynomials P(U, V) of F(U, V) satisfy finitely many asymptotic identities, namely, identities of the following type, P(X− k, A0 + A1 X + … + AN − 1 XN − 1 + YXN) = A(X, Y)ϵ R[X, Y], which ‘capture’ the whole set of asymptotic values of F. 相似文献
16.
Oleg T. Izhboldin 《manuscripta mathematica》2000,102(1):41-52
Let F be a field of characteristic ≠2 and φ be a quadratic form over F. By X
φ we denote the projective variety given by the equation φ=0. For each positive even integer d≥8 (except for d=12) we construct a field F and a pair φ, ψ of anisotropic d-dimensional forms over F such that the Chow motives of X
φ and X
ψ coincide but . For a pair of anisotropic (2
n
-1)-dimensional quadrics X and Y, we prove that existence of a rational morphism Y→X is equivalent to existence of a rational morphism Y→X.
Received: 27 September 1999 / Revised version: 27 December 1999 相似文献
17.
Let X,Y be sets with quasiproximities X? and Y? (where A?B is interpreted as “B is a neighborhood of A”). Let f,g:X→Y be a pair of functions such that whenever CY?D, then f−1[C]X?g−1[D]. We show that there is then a function h:X→Y such that whenever CY?D, then f−1[C]X?h−1[D], h−1[C]X?h−1[D] and h−1[C]X?g−1[D]. Since any function h that satisfies h−1[C]X?h−1[D] whenever CY?D, is continuous, many classical “sandwich” or “insertion” theorems are corollaries of this result. The paper is written to emphasize the strong similarities between several concepts
- •
- the posets with auxiliary relations studied in domain theory;
- •
- quasiproximities and their simplification, Urysohn relations; and
- •
- the axioms assumed by Katětov and by Lane to originally show some of these results.
18.
《Topology》2003,42(6):1205-1227
Let k be a knot in S3. There is an epimorphism from π1(S3−k) onto a free product of two nontrivial cyclic groups sending a meridian to an element of length two iff k has property Q (Topology of Manifolds, Markham, Chicago, IL, 1970, pp. 195-199) that is if there is a closed surface F in S3 containing k, such that k is imprimitive in H1(X) and in H1(Y) where X and Y are the closures of the components of S3−F. We give answers to questions of Simon (1970) about properties Q, Q∗ and Q∗∗. Epimorphisms from knot groups onto torus knot groups are also studied and some results on property P and surgery are included. 相似文献
19.
20.
Nejla Ozkaya Turhan 《Journal of Computational and Applied Mathematics》2012,236(9):2259-2267
In this study, two independent samples X1,X2,…,Xn and Y1,Y2,…,Ym with respective distribution functions F and Q are considered. The joint asymptotic distributions of exceedance statistics defined as the number of Y observations falling into a random interval of order statistics constructed from the X sample is investigated. The results can be used in the context of a two-sample problem. 相似文献