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1.
We point out that the formalism of the trace map and reduction modulo p can be used to give a short proof for the fact first proved by Ogg that is not a Weierstrass point on X0(pM) where p is a prime not dividing M and the genus of X0(M) is zero.  相似文献   

2.
3.
Let H be an atomic monoid. For let denote the set of all with the following property: There exist atoms (irreducible elements) u 1, …, u k , v 1, …, v m H with u 1· … · u k = v 1 · … · v m . We show that for a large class of noetherian domains satisfying some natural finiteness conditions, the sets are almost arithmetical progressions. Suppose that H is a Krull monoid with finite cyclic class group G such that every class contains a prime (this includes the multiplicative monoids of rings of integers of algebraic number fields). We show that, for every , max which settles Problem 38 in [4]. Authors’ addresses: W. Gao, Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China; A. Geroldinger, Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit?t Graz, Heinrichstra?e 36, 8010 Graz, Austria  相似文献   

4.
For a probability measure μ on a subset of , the lower and upper Lq-dimensions of order are defined by We study the typical behaviour (in the sense of Baire’s category) of the Lq-dimensions and . We prove that a typical measure μ is as irregular as possible: for all q ≥ 1, the lower Lq-dimension attains the smallest possible value and the upper Lq-dimension attains the largest possible value.  相似文献   

5.
For a positive integer N, we define the N-rank of a non singular integer d × d matrix A to be the maximum integer r such that there exists a minor of order r whose determinant is not divisible by N. Given a positive integer r, we study the growth of the minimum integer k, such that A k I has N-rank at most r, as a function of N. We show that this integer k goes to infinity faster than log N if and only if for every eigenvalue λ which is not a root of unity, the sum of the dimensions of the eigenspaces relative to eigenvalues which are multiplicatively dependent with λ and are not roots of unity, plus the dimensions of the eigenspaces relative to eigenvalues which are roots of unity, does not exceed dr − 1. This result will be applied to recover a recent theorem of Luca and Shparlinski [6] which states that the group of rational points of an ordinary elliptic curve E over a finite field with q n elements is almost cyclic, in a sense to be defined, when n goes to infinity. We will also extend this result to the product of two elliptic curves over a finite field and show that the orders of the groups of rational points of two non isogenous elliptic curves are almost coprime when n approaches infinity. Author’s address: Dipartimento di Matematica e Informatica, Via Delle Scienze 206, 33100 Udine, Italy  相似文献   

6.
The classical n-variable Kloosterman sums over the finite field F p give rise to a lisse -sheaf Kl n+1 on , which we call the Kloosterman sheaf. Let L p (G m, F p , Sym k Kl n+1, s) be the L-function of the k-fold symmetric product of Kl n+1. We construct an explicit virtual scheme X of finite type over Spec Z such that the p-Euler factor of the zeta function of X coincides with L p (G m, F p , Sym k Kl n+1, s). We also prove similar results for and . The research of L. Fu is supported by the NSFC (10525107).  相似文献   

7.
 We prove that any basis of a non-degenerate 4-dimensional lattice with sufficiently small (positive) homogeneous minimum can be represented in the form DOTU. This is of interest in connection with Minkowski’s conjecture about the product of inhomogeneous linear forms. Received 23 September 2001 RID="a" ID="a" Dedicated to Prof. Edmund Hlawka on the occasion of his 85th birthday  相似文献   

8.
We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1kn. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.This revised version was published online in October 2004 with a corrected Received date.  相似文献   

9.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞.  相似文献   

10.
Characterization of q-Orthogonal Polynomials. Im Anschluß an die Arbeit Orthogonalpolynome in x und q–x als Lösungen von reellen q-Operatorgleichungen zweiter Ordnung (Monatsh. Math. 132, 123–140 (2001); im folgenden als [4] zitiert) werden alle Möglichkeiten für q-Orthogonalpolynome in x als Lösungen von q-Operatorgleichungen zweiter Ordnung angegeben (Orthogonalität im positiv definiten Sinne). Dabei erfolgt die Numerierung der Abschnitte und die Angabe der Formel-nummern unter Einbeziehung von [4].  相似文献   

11.
We prove that the submodule in K-theory which gives the exact value of the L-function by the Beilinson regulator map at non-critical values for Hecke characters of imaginary quadratic fields K with cl (K) = 1(p-local Tamagawa number conjecture) satisfies that the length of its coimage under the local Soulé regulator map is the p-adic valuation of certain special values of p-adic L-functions associated to the Hecke characters. This result yields immediately, up to Jannsens conjecture, an upper bound for in terms of the valuation of these p-adic L-functions, where Vp denotes the p-adic realization of a Hecke motive.Received: 4 June 2003  相似文献   

12.
For i = 1, , r, let f i be newforms of weight 2k i for Γ0(N i ) with trivial character. We consider the simultaneous non-vanishing problem for the central values of twisted L-functions of f i . By using the Shimura correspondence, we give a certain relation between this problem and the kernel fields of 2-adic Galois representations associated to modular forms. Received: 28 January 2006  相似文献   

13.
In the present paper we discuss in detail the cohomogeneity one isometric actions of the Lie groups SU(3) × SU(3) and SU(3) on the exceptional compact symmetric spaces G2 and G2/SO(4), respectively. We show that the principal orbits coincide with the tubular hypersurfaces around the totally geodesic singular orbits, and the symmetric spaces G2 and G2/SO(4) can be thought of as compact tubes around SU(3) and P2, respectively. Moreover, we determine the radii of these tubes and describe the shape operators of the principal orbits. Finally, we apply these results to compute the volumes of the two symmetric spaces.The author was partially supported by the Hungarian National Science and Research Foundation OTKA T032478.  相似文献   

14.
For q ≥ 0, Olsen [1] has attained the exact rate of convergence of the L q -spectrum of a self-similar measure and showed that the so-called empirical multifractal moment measures converges weakly to the normalized multifractal measures. Unfortunately, nothing is known for q < 0. Indeed, the problem of analysing the L q - spectrum for q < 0 is generally considered significantly more difficult since the L q -spectrum is extremely sensitive to small variations of μ for q < 0. In [2] we showed that self-similar measures satisfying the Open Set Condition (OSC) are Ahlfors regular and, using this fact, we obtained the exact rate of convergence of the L q -spectrum of a self-similar measure satisfying the OSC for q < 0. In this paper, we apply the results from [2] to show the empirical multifractal q’th moment measures of self-similar measures satisfying the OSC converges weakly to the normalized multifractal Hausdorff measures for q < 0. Authors’ addresses: Jiaqing Xiao, School of Science, Wuhan University of Technology, Wuhan 430070, China; Wu Min, School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China  相似文献   

15.
Suppose that {T t  : t  ≥  0} is a symmetric diffusion semigroup on L 2(X) and denote by its tensor product extension to the Bochner space , where belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf–Dunford–Schwartz ergodic theorem and show that this extends to a maximal theorem for analytic continuations of on . As an application, we show that such continuations exhibit pointwise convergence.  相似文献   

16.
Let F (s) be a function belonging to the Selberg class. For a primitive Dirichlet character , we can define the -twist F(s) of F (s). If F(s) also belongs to the Selberg class and satisfies some other conditions then there is a relation between the zeros of F (s) and the zeros F(s). Further we give an operator theoretic interpretation of this relation according to A. Connes study.Received: 5 January 2004  相似文献   

17.
Let a,b be given, multiplicatively independent positive integers and let >0. In a recent paper jointly with Y. Bugeaud we proved the upper bound exp(n) for g.c.d.(an–1, bn–1); shortly afterwards we generalized this to the estimate g.c.d.(u–1,v–1)v) for multiplicatively independent S-units u,vZ. In a subsequent analysis of those results it turned out that a perhaps better formulation of them may be obtained in terms of the language of heights of algebraic numbers. In fact, the purposes of the present paper are: to generalize the upper bound for the g.c.d. to pairs of rational functions other than {u–1,v–1} and to extend the results to the realm of algebraic numbers, giving at the same time a new formulation of the bounds in terms of height functions and algebraic subgroups of Gm2.  相似文献   

18.
We consider a rational surface Xr, obtained by blowing up 2 along a curvilinear zero-dimensional subscheme of length r of the regular locus of a reduced irreducible plane curve of degree d, with d 4; and we give sufficient conditions for d-standard classes to be very ample (resp. base point free or non special) on such a rational surface Xr.Postdoctoral Fellow of the Fund for Scientific Research-Flanders (Belgium).  相似文献   

19.
We consider the mixed problem,
in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data, f D , has one derivative in L p (D) of the boundary and the Neumann data, f N , is in L p (N). We find a p 0 > 1 so that for p in an interval (1, p 0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L p . L. Lanzani, L. Capogna and R. M. Brown were supported, in part, by the U.S. National Science Foundation.  相似文献   

20.
In this paper we prove the unique factorization of certain subsemigroups of the extended Selberg class of L-functions. These semigroups are generated by the functions of degree 0 and 1. We also consider extensions of such results and applications to classical L-functions.  相似文献   

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