首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 78 毫秒
1.
On the Poles of Igusa's Local Zeta Function for Algebraic Sets   总被引:1,自引:0,他引:1  
Let K be a p-adic field, let Z (s, f), sC, with Re(s) > 0,be the Igusa local zeta function associated to f(x) = (f1(x),..., fl(x)) [K (x1, ..., xn)]l, and let be a Schwartz–Bruhatfunction. The aim of this paper is to describe explicitly thepoles of the meromorphic continuation of Z (s, f). Using resolutionof singularities it is possible to express Z (s, f) as a finitesum of p-adic monomial integrals. These monomial integrals arecomputed explicitly by using techniques of toroidal geometry.In this way, an explicit list of the candidates for poles ofZ (s, f) is obtained. 2000 Mathematics Subject Classification11S40, 14M25, 11D79.  相似文献   

2.
Let q and N be integers, let a be an integer coprime to q, andlet zN be defined implicitly by . We show that for large N, an integer n has at least one divisord with q d N and d a(mod q) with probability approximately(zN), where denotes the distribution function of the GaussianLaw. This solves a conjecture of Hall. 1991 Mathematics SubjectClassification 11N25, 11N37.  相似文献   

3.
Let Y be a locally compact group, Aut(Y) be the group of topologicalautomorphisms of Y and (Y) be the set of continuous positivedefinite functions on Y which have unit value at the identity.A function (Y2) is said to be of product type if there aresuch functions j (Y) that (u, v) = 1(u)2(v). Define the mappingT: Y2 Y2 by the formula T(u, v) = (A1 uA2 v, A3 u A4 v), whereAj Aut(Y), and assume that T is a one-to-one transform. K.Schmidt proved: (i) if both (u, v) and (T(u, v)) are of producttype, then the functions j are infinitely divisible; (ii) ifY is Abelian, both (u, v) and (T(u, v)) are of product type,and (u, v) 0, then the functions j are Gaussian. We show thatstatement (i), generally, is not valid, but K. Schmidt's proofholds true if (u, v) 0. We also give another proof of statement(ii). Our proof uses neither the Levy–Khinchin formulafor a continuous infinitely divisible positive definite functionnor (i) on which K. Schmidt's proof is based.  相似文献   

4.
Generalized Catalan Numbers, Weyl Groups and Arrangements of Hyperplanes   总被引:1,自引:0,他引:1  
For an irreducible, crystallographic root system in a Euclideanspace V and a positive integer m, the arrangement of hyperplanesin V given by the affine equations (, x) = k, for and k =0, 1, ..., m, is denoted here by . The characteristic polynomial of is related in the paper to that of the Coxeter arrangement A(corresponding to m = 0), and the number of regions into whichthe fundamental chamber of A is dissected by the hyperplanesof is deduced to be equal to the product , where e1,e2, ..., el are the exponents of and h is the Coxeter number.A similar formula for the number of bounded regions follows.Applications to the enumeration of antichains in the root posetof are included. 2000 Mathematics Subject Classification 20F55(primary), 05A15, 52C35 (secondary).  相似文献   

5.
Recurrence, Dimension and Entropy   总被引:2,自引:0,他引:2  
Let (A, T) be a topologically mixing subshift of finite typeon an alphabet consisting of m symbols and let :A Rd be a continuousfunction. Denote by (x) the ergodic limit when the limit exists. Possible ergodic limits arejust mean values dµ for all T-invariant measures. Forany possible ergodic limit , the following variational formulais proved: where hµ denotes the entropy of µ and htop denotestopological entropy. It is also proved that unless all pointshave the same ergodic limit, then the set of points whose ergodiclimit does not exist has the same topological entropy as thewhole space A  相似文献   

6.
The weak compactness of the composition operator C(f) = f acting on the uniform algebra of analytic uniformly continuousfunctions on the unit ball of a Banach space with the approximationproperty is characterized in terms of . The relationship betweenweak compactness and compactness of these composition operatorsand general homomorphisms is also discussed. 2000 MathematicsSubject Classification 46J15 (primary), 46E15, 46G20 (secondary).  相似文献   

7.
Let = (f, g):(Cn+ 1,0) (C2, 0) be a pair of holomorphic germswith no blowing up in codimension 0. (Two examples are the following: defines an isolated complete intersection singularity; g =lN where is a generic linear form with respect to f and N>0.) We study how the Milnor fibrations of the germs (:ß)= gf are related to each other when (:ß)varies in P1. More precisely, we construct isotopic subfibrationsor subfibres of the Milnor fibrations of any two such germs.The proofs are based on the precise study of the subdiscs ofcomplex lines meeting a fixed complex plane curve germ transversally,generalizing Lê's work on the Cerf diagram. 2000 MathematicalSubject Classification: 32S55, 32S15, 32S30.  相似文献   

8.
For any positive integer n we let P(n) be the largest primefactor of n. We improve and generalize several results of P.Erds and C. Stewart on P(n!+1). In particular, we show thatlim supninfin; P(n!+1)/n2.5, which improves their lower boundof lim supninfin; P(n!+1)/n2. 2000 Mathematics Subject Classification11A05, 11A07, 11J86.  相似文献   

9.
Let G be a group, and let Fn[G] be the free G-group of rankn. Then Fn[G] is just the natural non-abelian analogue of thefree ZG-module of rank n, and correspondingly the group n(G)of equivariant automorphisms of Fn[G] is a natural analogueof the general linear group GLn(ZG). The groups n(G) have beenstudied recently in [4, 8, 5]. In particular, in [5] it wasshown that if G is not finitely presentable (f.p.) then neitheris n(G), and conversely, that n(G) is f.p. if G is f.p. andn2. It is a common phenomenon that for small ranks the automorphismgroups of free objects may behave unstably (see the survey article[2]), and the main aim of the present paper is to show thatthis turns out to be the case for the groups 2(G).  相似文献   

10.
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号