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1.
Consider a classical cusp eigenform f= n=1 a n (f)q n of weight k2 for 0(N) with a Dirichlet character mod N, and let L f (s,)= n=1 (n)a n (f)n -s denote the L-function of f twisted with an arbitrary Dirichlet character . For a prime number p5, consider a family of cusp eigenforms f (k) of weight k , k {f (k)= n=1 a n (f (k))q n } containing f=f (k), such that the Fourier coefficients a n (f (k)) are given by certain p-adic analytic functions k a n (f (k)). The purpose of this paper is to construct a two variable p-adic L function attached to Colemans family {f (k)} of cusp eigenforms of a fixed positive slope =v p ( p )>0 where p = p (k ) is an eigenvalue (which depends on k ) of the Atkin operator U=U p . Our p-adic L-function interpolates the special values L f(k)(s,) at points (s,k ) with s=1,2,...,k -1. We give a construction using the Rankin-Selberg method and the theory of p-adic integration on a profinite group Y with values in an affinoid K-algebra A, where K is a fixed finite extension of Q p . Our p-adic L-functions are p-adic Mellin transforms of certain A-valued measures. In their turn, such measures come from Eisenstein distributions with values in certain Banach A-modules M =M (N;A) of families of overconvergent forms over A. To Robert Alexander Rankin in memoriam  相似文献   

2.
For a domain R4 and a compact Riemannian manifold NRk without boundary, if uW2,2(,N) is an extrinsic (or intrinsic, respectively) biharmonic map, then uC(,N).in final form: 1 August 2003  相似文献   

3.
Suppose X. We construct examples of bounded sets MX, such that These examples show that the previous results of the authors on quantitative versions of Kreins theorem are optimal.Mathematics Subject Classification (2000):46B20, 46B26A. S. Granero supported by DGICYT grant BFM2001-1284. P. Hájek supported by GAR 201/01/1198, A 101 92 05 and UPV grant PPI-02-02.  相似文献   

4.
The following result is proved: Let be a n-dimensional C1-submanifold of RN which is domain of a given nRN-valued map of class C1. Then the set of all points P such that (P) is non-zero, simple and enveloped by TP is C2-rectifiable. As a corollary we get a criterion for the C2-rectifiability of a rectifiable set based on the rectifiability of some generalized Gauss lift to the Grassmanian bundle RN×G(N,n). Mathematics Subject Classification (2000) Primary 49Q15, 53A07; Secondary 49Q20, 49N60  相似文献   

5.
We define K-homology groups K * () for small C * -categories in terms of Hilbert modules over the C * -category . We also define a functor A f from the category of small C * -categories into the category of C * -algebras and show that there is a natural isomorphism . In addition, we give an easy construction of a functor from the category of C * -algebras into the category of symmetric spectra which represents K-homology, i.e. we show that the functor comes with a natural isomorphism for C * -algebras A. It then follows that the composition A f provides a functor that can be used in the Davis-Lück approach for constructing the Baum-Connes map.  相似文献   

6.
Let G =K A N be an Iwasawa decomposition of a connected, noncompact real semisimple Lie group with finite center and let M be the centralizer of A in K . B. Kostant proved that for every irreducible M-spherical K-module V there exists a unique d (the Kostant degree of V) such that V can be realized as a submodule of the space of all -harmonic homogeneous polynomials of degree d on . Here is a Cartan decomposition of the complexification of the Lie algebra of G .In this paper we give an algorithm to obtain a highest weight vector from any M-invariant vector in an irreducible M-spherical K-module. This algorithm allows us to compute a sharp bound for the Kostant degree d(v) of any M-invariant vector v in a locally finite M-spherical K-module V. The method computes d(v) effectively for any V if G is locally isomorphic to SO(n,1) and for if G is locally isomorphic to SU(n,1).Partially supported by Agencia Córdoba Ciencia and CONICET Mathematics Subject Classification (2000):Primary 22E46, Secondary 43A85  相似文献   

7.
Let s 0 and let + s be the set of functions x defined on a finite interval I and such that, for all collections of s + 1 pairwise different points t 0,..., t s I, the corresponding divided differences [x; t 0,...,t s ] of order s are nonnegative. Let + s B p + s B p, 1 p where B p is a unit ball in the space L p, and let + s L q + s L q, 1 q . For every s 3 and 1 q p , we determine the exact orders of the shape-preserving Kolmogorov widths {x - y} \right\ L_q , $$]]>, where M n is the collection of all affine linear manifolds M n in L q such that dim M n n and M n + s L q .Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 901–926, July, 2004.  相似文献   

8.
There have been many results obtained so far for the mean square of the (absolute) value of the Dirichlet L-function L(s,) in the critical strip 0<<1, especially on the critical line , but relatively few results were known for discrete mean value of |L(1,)|2 till W. Zhang had published papers improving the error term step by step, which have recently been superseded by M. Katsurada and K.Matsumoto in which they succeeded in deriving an asymptotic formula for 0|L(1,)|2. The object of our paper is to point out a structural property contained in the formation of the mean square, to find out the niryana–the true body of the above sum.Dedicated to Professor Jean Louis Nicolás on his sixtieth birthdayin final form: 7 October 2003  相似文献   

9.
Let S be a minimal surface of general type with pg=0 and K2=6, such that its bicanonical map is not birational. The map is a morphism of degree 4 onto a surface. The case of deg = 4 is completely classified in [Topology, 40 (5) (2001), 977–991] and the present paper completes the characterization of these surfaces. It is proven that the degree of cannot be equal to 3, and the geometry of surfaces with deg = 2 is analysed in detail. The last section contains three examples of such surfaces, two of which appear to be new.Mathematics Subject Classification (2000): 14J29  相似文献   

10.
Summary We prove that, for any Tychonoff X, the space Cp(X) is K-analytic if and only if it has a compact cover {Kp: p } such that Kp subset Kq whenever p,q and p q. Applying this result we show that if Cp(X) is K-analytic then Cp(X) is K-analytic as well. We also establish that a space Cp(X) is K-analytic and Baire if and only if X is countable and discrete.  相似文献   

11.
Given a von Neumann algebra M and a W*-correspondence E over M, we construct an algebra H(E) that we call the Hardy algebra of E. When M= =E, H(E) is the classical Hardy space H of bounded analytic functions on the unit disc. When M= and E= H(E) is the free semigroup algebra studied by Popescu, Davidson and Pitts and many others. We show that given any faithful normal representation of M on a Hilbert space H there is a natural correspondence E over the commutant (M), called the -dual of E, and that H(E) can be realized in terms of (B(H)-valued) functions on the open unit ball ((E)*) in the space of adjoints of elements in E. We prove analogues of the Nevanlinna-Pick theorem in this setting and discover other aspects of the value distribution theory for elements in H(E). We also analyze the boundary behavior of elements in H(E) and obtain generalizations of the Sz.-Nagy–Foia functional calculus and the functional calculus of Popescu for c.n.c. row contractions. The correspondence E has a dual that is naturally isomorphic to E and the commutants of certain, so-called induced representations of H(E) can be viewed as induced representations of H(E). For these induced representations a double commutant theorem is proved.Supported in part by grants from the National Science Foundation and from the U.S.-Israel Binational Science Foundation.Supported in part by the U.S.-Israel Binational Science Foundation and by the Fund for the Promotion of Research at the Technion.Revised version: 11 March 2004  相似文献   

12.
Let be a bounded domain in Cn and let L2h() be the L2-holomorphic functions on . We show that the envelope of holomorphy and the L2h()-envelope of holomorphy of differ by at most a pluripolar set.Mathematics Subject Classification (2000): 32D10, 32A36, 32U30This article is based on work the author did during his Ph.D. studies at the University of Michigan under the supervision of John Erik Fornæss.  相似文献   

13.
Let p be an odd prime number and let n be an arbitrary positive integer. We prove that there exists a p-group whose mod-p cohomology ring has a nilpotent element H2() satisfying n0,n+p–1=0. As a corollary, we exhibit a p-group whose mod-p cohomology ring contains an element of nilpotency degree n+1.Mathematical Subject Classification (2000): 20J06, 20D15, 55R40To Phuong and Nin  相似文献   

14.
We introduce and solve a natural geometrical extremal problem. For the set E (n,w) = {x n {0,1} n : x n has w ones } of vertices of weight w in the unit cube of n we determine M (n,k,w) max{|U k n E(n,w)|:U k n is a k-dimensional subspace of n . We also present an extension to multi-sets and explain a connection to a higher dimensional Erds–Moser type problem.  相似文献   

15.
The Markov moment problem is to characterize sequences admitting the representation sn=01xnf(x)dx, where f(x) is a probability density on [0,1] and 0f(x)c for almost all x. There are well-known characterizations through complex systems of non-linear inequalities on {sn}. Necessary and sufficient linear conditions are the following: s0=1, and for all and . Here, is the forward difference operator. This result is due to Hausdorff. We give a new proof with some ancillary results, for example, characterizing monotone densities. Then we make the connection to de Finettis theorem, with characterizations of the mixing measure.in final form: 18 June 2003  相似文献   

16.
Let Z t , t 0 be a strictly stable process on with index (0, 2]. We prove that for every p > , there exists = , p and such that
where || Z|| p stands for the strong p-variation of Z on [0,1]. The critical exponent p , takes a different shape according as | Z| is a subordinator and p > 1, or not. The small ball constant is explicitly computed when p > 1, and a lower bound on is easily obtained in the general case. In the symmetric case and when p > 2, we can also give an upper bound on in terms of the Brownian small ball constant under the (1/p)-Höder semi-norm. Along the way, we remark that the positive random variable is not necessarily stable when p > 1, which gives a negative answer to an old question of P. E. Greenwood.10  相似文献   

17.
Let M be a Riemannian manifold. A complete geodesic on M means that :(-,+)M is a normalized geodesic. In this paper, we prove that on (S2,g) with positive curvature, any two complete geodesics must intersect an infinite number of times, and a complete geodesic must self-intersect an infinite number of times. Mathematics Subject Classification (2000) 53C40 (53C22)  相似文献   

18.
Summary Let G be a finite group. Order components of G were introduced in Chen [5]. Let OC(G) be the set of order components of G. Some finite groups are characterizable by their order components. This assertion was proved for the simple groups PSU(p,q), where p=3, 5, 7 and 11. In this paper, we prove that the simple groups PSU(p,q) can be uniquely determined by their order components, where p&ge;13 is a prime number. Main consequences of our results are the validity of a conjecture of J. G. Thompson and another conjecture of W. Shi and J. Bi for the groups under consideration.  相似文献   

19.
We prove Lp estimates (Theorem 1.8) for the Walsh model of the biest, a trilinear multiplier with singular symbol. The corresponding estimates for the Fourier model will be obtained in the sequel [11] biest of this paper.  相似文献   

20.
A function analytic in the unit disk is called (p, A)-lacunary if the inequalities n k Ak p hold for all k 0 with some 1 < p < and A > 0. In this paper, for 1 < p < 2 and A > 0, we construct a (p, A)-lacunary function f 1,p,A (z) decreasing as x 1 – 0 at a rate close to the optimal rate for (p, A)-lacunary functions. Bibliography: 6 titles.  相似文献   

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