共查询到20条相似文献,搜索用时 31 毫秒
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Clemens Fuchs 《Indagationes Mathematicae》2009,20(2):217-231
In this paper we give effective upper bounds for the degree k of divisors (over ?) of generalized Laguerre polynomials Lαn(x), i.e. of for α = −tn − s − 1 and α = tn + s with t,s ∈ ?, t = O(log k), s = O(k log k) and k sufficiently large. 相似文献
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Kazushi Yoshitomi 《Indagationes Mathematicae》2005,16(2):289-299
Let q ∈ {2, 3} and let 0 = s0 < s1 < … < sq = T be integers. For m, n ∈ Z, we put ¯m,n = {j ∈ Z| m? j ? n}. We set lj = sj − sj−1 for j ∈ 1, q. Given (p1,, pq) ∈ Rq, let b: Z → R be a periodic function of period T such that b(·) = pj on sj−1 + 1, sj for each j ∈ 1, q. We study the spectral gaps of the Jacobi operator (Ju)(n) = u(n + 1) + u(n − 1) + b(n)u(n) acting on l2(Z). By [λ2j , λ2j−1] we denote the jth band of the spectrum of J counted from above for j ∈ 1, T. Suppose that pm ≠ pn for m ≠ n. We prove that the statements (i) and (ii) below are equivalent for λ ∈ R and i ∈ 1, T − 1. 相似文献
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R. Nair 《Indagationes Mathematicae》2004,15(3):373-381
Given a subset S of Z and a sequence I = (In)n=1∞ of intervals of increasing length contained in Z, let
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It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle Ed1,…,dn on PN defined as the kernel of a general epimorphism
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Çetin Ürti? 《Journal of Number Theory》2007,125(1):149-181
We study the arithmeticity of special values of L-functions attached to cuspforms which are Hecke eigenfunctions on hermitian quaternion groups Sp∗(m,0) which form a reductive dual pair with G=O∗(4n). For f1 and f2 two cuspforms on H, consider their theta liftings θf1 and θf2 on G. Then we compute a Rankin-Selberg type integral and obtain an integral representation of the standard L-function:
G〈θf1⋅Es,θf2〉=H〈f1,f2〉⋅Lstd(f1,s). 相似文献
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Songzhe Lian Chunling Cao Hongjun Yuan 《Journal of Mathematical Analysis and Applications》2008,342(1):27-38
The authors of this paper study the Dirichlet problem of the following equation
ut−div(|u|ν(x,t)∇u)=f−|u|p(x,t)−1u. 相似文献
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Jian-Lin Li 《Journal of Functional Analysis》2008,255(11):3125-3148
The self-affine measure μM,D corresponding to an expanding matrix M∈Mn(R) and a finite subset D⊂Rn is supported on the attractor (or invariant set) of the iterated function system {?d(x)=M−1(x+d)}d∈D. The spectral and non-spectral problems on μM,D, including the spectrum-tiling problem implied in them, have received much attention in recent years. One of the non-spectral problem on μM,D is to estimate the number of orthogonal exponentials in L2(μM,D) and to find them. In the present paper we show that if a,b,c∈Z, |a|>1, |c|>1 and ac∈Z?(3Z),
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Shih Ping Tung 《Journal of Number Theory》2010,130(4):912-929
In this paper we study the maximum-minimum value of polynomials over the integer ring Z. In particular, we prove the following: Let F(x,y) be a polynomial over Z. Then, maxx∈Z(T)miny∈Z|F(x,y)|=o(T1/2) as T→∞ if and only if there is a positive integer B such that maxx∈Zminy∈Z|F(x,y)|?B. We then apply these results to exponential diophantine equations and obtain that: Let f(x,y), g(x,y) and G(x,y) be polynomials over Q, G(x,y)∈(Q[x,y]−Q[x])∪Q, and b a positive integer. For every α in Z, there is a y in Z such that f(α,y)+g(α,y)bG(α,y)=0 if and only if for every integer α there exists an h(x)∈Q[x] such that f(x,h(x))+g(x,h(x))bG(x,h(x))≡0, and h(α)∈Z. 相似文献
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The hypersurfaces of degree d in the projective space Pn correspond to points of PN, where . Now assume d=2e is even, and let X(n,d)⊆PN denote the subvariety of two e-fold hyperplanes. We exhibit an upper bound on the Castelnuovo regularity of the ideal of X(n,d), and show that this variety is r-normal for r?2. The latter result is representation-theoretic, and says that a certain GLn+1-equivariant morphism
Sr(S2e(Cn+1))→S2(Sre(Cn+1)) 相似文献
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Tetsuo Harada 《Linear algebra and its applications》2007,425(1):102-108
Let A and B be invertible positive elements in a II1-factor A, and let μs(·) be the singular number on A. We prove that
exp∫Klogμs(AB)ds?exp∫Ilogμs(A)ds·exp∫Jlogμs(B)ds, 相似文献
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D.S. Lubinsky 《Journal of Mathematical Analysis and Applications》2006,314(1):266-285
We obtain the rate of growth of the largest eigenvalues and Euclidean condition numbers of the Hankel matrices for a general class of even exponential weights W2=exp(−2Q) on an interval I. As particular examples, we discuss Q(x)=α|x| on I=R, and Q(x)=(d2−x2)−α on I=[−d,d]. 相似文献
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We consider, for p∈(1,2) and q>1, self-similar singular solutions of the equation vt=div(|∇v|p−2∇v)−vq in Rn×(0,∞); here by self-similar we mean that v takes the form v(x,t)=t−αw(|x|t−αβ) for α=1/(q−1) and β=(q+1−p)/p, whereas singular means that v is non-negative, non-trivial, and for all x≠0. That is, we consider the ODE problem
(0.1) 相似文献
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Let (|q|<1). For k∈N it is shown that there exist k rational numbers A(k,0),…,A(k,k−1) such that
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We prove that the divisor function d(n) counting the number of divisors of the integer n is a good weighting function for the pointwise ergodic theorem. For any measurable dynamical system (X, A, ν, τ) and any f ∈ L p (ν), p > 1, the limit exists ν-almost everywhere. The proof is based on Bourgain’s method, namely the circle method based on the shift model. Using more elementary ideas we also obtain similar results for other arithmetical functions, like the θ(n) function counting the number of squarefree divisors of n and the generalized Euler totient function J s (n) = Σ d|n d s μ(n/d), s > 0.
相似文献
$$\mathop {\lim }\limits_{n \to \infty } \frac{1}{{\Sigma _{k = 1}^nd\left( k \right)}}\sum\limits_{k = 1}^n {d\left( k \right)f\left( {{\tau ^k}x} \right)} $$
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We consider the random variable Zn,α=Y1+2αY2+?+nαYn, with α∈R and Y1,Y2,… independent and exponentially distributed random variables with mean one. The distribution function of Zn,α is in terms of a series with alternating signs, causing great numerical difficulties. Using an extended version of the saddle point method, we derive a uniform asymptotic expansion for P(Zn,α<x) that remains valid inside (α≥−1/2) and outside (α<−1/2) the domain of attraction of the central limit theorem. We discuss several special cases, including α=1, for which we sharpen some of the results in Kingman and Volkov (2003). 相似文献
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Let N denote the set of positive integers. The asymptotic density of the set A⊆N is d(A)=limn→∞|A∩[1,n]|/n, if this limit exists. Let AD denote the set of all sets of positive integers that have asymptotic density, and let SN denote the set of all permutations of the positive integers N. The group L? consists of all permutations f∈SN such that A∈AD if and only if f(A)∈AD, and the group L* consists of all permutations f∈L? such that d(f(A))=d(A) for all A∈AD. Let be a one-to-one function such that d(f(N))=1 and, if A∈AD, then f(A)∈AD. It is proved that f must also preserve density, that is, d(f(A))=d(A) for all A∈AD. Thus, the groups L? and L* coincide. 相似文献
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Leigh C. Becker 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):1892-1912
The structure of the resolvent R(t,s) for a weakly singular matrix function B(t,s) is determined, where B(t,s) is the kernel of the linear Volterra vector integral equation
(E ) 相似文献