共查询到20条相似文献,搜索用时 46 毫秒
1.
Hae-Sang Sun 《Journal of Number Theory》2010,130(1):10-26
We extend the result of Anglès (2007) [1], namely for the Iwasawa power series . For the derivative , a numerical polynomial Q on Zp, and a prime π in over p, we show that if and only if i.e. for all x∈Zp. This result comes from a similar assertion for the power series attached to the Γ-transform of a p-adic measure which is related to a certain rational function in . 相似文献
2.
Zhichun Zhai 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2611-2630
Let be the space of solutions to the parabolic equation having finite norm. We characterize nonnegative Radon measures μ on having the property , 1≤p≤q<∞, whenever . Meanwhile, denoting by v(t,x) the solution of the above equation with Cauchy data v0(x), we characterize nonnegative Radon measures μ on satisfying , β∈(0,n), p∈[1,n/β], q∈(0,∞). Moreover, we obtain the decay of v(t,x), an isocapacitary inequality and a trace inequality. 相似文献
3.
Zhi-Hong Sun 《Journal of Number Theory》2009,129(3):499-550
Let be a prime and a,b∈Z with a2+b2≠p. Suppose p=x2+(a2+b2)y2 for some integers x and y. In the paper we develop the calculation technique of quartic Jacobi symbols and use it to determine . As applications we obtain the congruences for modulo p and the criteria for (if ), where {Un} is the Lucas sequence given by U0=0, U1=1 and Un+1=bUn+k2Un−1(n?1). We also pose many conjectures concerning , or . 相似文献
4.
Kui Liu 《Journal of Number Theory》2011,131(12):2247-2261
Let be the error term of the Riesz mean of the symmetric square L-function. We give the higher power moments of and show that if there exists a real number A0:=A0(ρ)>3 such that , then we can derive asymptotic formulas for , 3?h<A0, h∈N. Particularly, we get asymptotic formulas for , h=3,4,5 unconditionally. 相似文献
5.
Let p∈(1,∞), q∈[1,∞), s∈R and . In this paper, the authors establish the φ-transform characterizations of Besov-Hausdorff spaces and Triebel-Lizorkin-Hausdorff spaces (q>1); as applications, the authors then establish their embedding properties (which on is also sharp), smooth atomic and molecular decomposition characterizations for suitable τ. Moreover, using their atomic and molecular decomposition characterizations, the authors investigate the trace properties and the boundedness of pseudo-differential operators with homogeneous symbols in and (q>1), which generalize the corresponding classical results on homogeneous Besov and Triebel-Lizorkin spaces when p∈(1,∞) and q∈[1,∞) by taking τ=0. 相似文献
6.
Siman Wong 《Journal of Number Theory》2010,130(10):2332-2340
Let M?5. For any odd prime power q and any prime ??q, we show that there are at least pairwise coprime D∈Fq[T] which are square-free and of odd degree ?M, such that ? does not divide the class number of the complex quadratic functions fields . 相似文献
7.
Let s∈R. In this paper, the authors first establish the maximal function characterizations of the Besov-type space with and τ∈[0,∞), the Triebel-Lizorkin-type space with p∈(0,∞), q∈(0,∞] and τ∈[0,∞), the Besov-Hausdorff space with p∈(1,∞), q∈[1,∞) and and the Triebel-Lizorkin-Hausdorff space with and , where t′ denotes the conjugate index of t∈[1,∞]. Using this characterization, the authors further obtain the local mean characterizations of these function spaces via functions satisfying the Tauberian condition and establish a Fourier multiplier theorem on these spaces. All these results generalize the existing classical results on Besov and Triebel-Lizorkin spaces by taking τ=0 and are also new even for Q spaces and Hardy-Hausdorff spaces. 相似文献
8.
Wansu Kim 《Journal of Number Theory》2011,131(7):1258-1275
Let K be a finite extension of Qp, and choose a uniformizer π∈K, and put . We introduce a new technique using restriction to to study flat deformation rings. We show the existence of deformation rings for -representations “of height ≤h” for any positive integer h, and prove that when h=1 they are isomorphic to “flat deformation rings”. This -deformation theory has a good positive characteristics analogue of crystalline representations in the sense of Genestier-Lafforgue. In particular, we obtain a positive characteristic analogue of crystalline deformation rings, and can analyze their local structure. 相似文献
9.
Let (|q|<1). For k∈N it is shown that there exist k rational numbers A(k,0),…,A(k,k−1) such that
10.
Yingjue Fang 《Journal of Number Theory》2011,131(11):2078-2080
Let E be a finite dimensional symplectic space over a local field of characteristic zero. We show that for every element in the metaplectic double cover of the symplectic group Sp(E), and are conjugate by an element of GSp(E) with similitude −1. 相似文献
11.
It was discovered some years ago that there exist non-integer real numbers q>1 for which only one sequence (ci) of integers ci∈[0,q) satisfies the equality . The set of such “univoque numbers” has a rich topological structure, and its study revealed a number of unexpected connections with measure theory, fractals, ergodic theory and Diophantine approximation.In this paper we consider for each fixed q>1 the set Uq of real numbers x having a unique representation of the form with integers ci belonging to [0,q). We carry out a detailed topological study of these sets. For instance, we characterize their closures, and we determine those bases q for which Uq is closed or even a Cantor set. We also study the set consisting of all sequences (ci) of integers ci∈[0,q) such that . We determine the numbers r>1 for which the map (defined on (1,∞)) is constant in a neighborhood of r and the numbers q>1 for which is a subshift or a subshift of finite type. 相似文献
12.
We investigate the distribution of the numbers x∈[1,p] for which all lie in a subset of the set of multiplicative inverses modulo a prime p. Here the ai are integers coprime to p and the numbers are distinct . 相似文献
13.
Jayanta Manoharmayum 《Journal of Number Theory》2009,129(5):1178-1190
Let F be a number field. Given a continuous representation with insoluble image we show, under moderate assumptions at primes dividing ?∞, that for some continuous representation which is unramified outside finitely many primes. We also establish level lowering when F is totally real, is the reduction of a nearly ordinary Hilbert modular form and is distinguished at ?. 相似文献
14.
15.
Gabriele Ranieri 《Journal of Number Theory》2008,128(6):1576-1586
Let p be an odd prime and q=pm, where m is a positive integer. Let ζq be a qth primitive root of 1 and Oq be the ring of integers in Q(ζq). In [I. Gaál, L. Robertson, Power integral bases in prime-power cyclotomic fields, J. Number Theory 120 (2006) 372-384] I. Gaál and L. Robertson show that if , where is the class number of , then if α∈Oq is a generator of Oq (in other words Z[α]=Oq) either α is equals to a conjugate of an integer translate of ζq or is an odd integer. In this paper we show that we can remove the hypothesis over . In other words we show that if α∈Oq is a generator of Oq then either α is a conjugate of an integer translate of ζq or is an odd integer. 相似文献
16.
17.
Zhi-Hong Sun 《Journal of Number Theory》2008,128(2):280-312
Let [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine , , and in terms of Euler and Bernoulli numbers. For example, we have
18.
Zhi-Hong Sun 《Journal of Number Theory》2005,113(1):10-52
Let be a prime, m∈Z and . In this paper we obtain a general criterion for m to be a quartic residue in terms of appropriate binary quadratic forms. Let d>1 be a squarefree integer such that , where is the Legendre symbol, and let εd be the fundamental unit of the quadratic field . Since 1942 many mathematicians tried to characterize those primes p so that εd is a quadratic or quartic residue . In this paper we will completely solve these open problems by determining the value of , where p is an odd prime, and . As an application we also obtain a general criterion for , where {un(a,b)} is the Lucas sequence defined by and . 相似文献
19.
Non-singular plane algebraic curves over with a Singer group of PGL(3,q) in their automorphism group are classified. Apart from three distinguished points, the set of -rational points of such curves can be partitioned into 2−(q2+q+1,q+1,1) designs each isomorphic to the finite projective plane . 相似文献
20.
Jimmy Tseng 《Journal of Number Theory》2009,129(12):3020-3025
For any real number θ, the set of all real numbers x for which there exists a constant c(x)>0 such that for all q∈Z\{0} is a 1/8-winning set. 相似文献