共查询到20条相似文献,搜索用时 15 毫秒
1.
Ana Cecilia de la Maza 《Journal of Number Theory》2008,128(8):2199-2213
Given a number field K and a subgroup G⊂K∗ of the multiplicative group of K, Silverman defined the G-height H(θ;G) of an algebraic number θ as
2.
Let f1,…,fd be an orthogonal basis for the space of cusp forms of even weight 2k on Γ0(N). Let L(fi,s) and L(fi,χ,s) denote the L-function of fi and its twist by a Dirichlet character χ, respectively. In this note, we obtain a “trace formula” for the values at integers m and n with 0<m,n<2k and proper parity. In the case N=1 or N=2, the formula gives us a convenient way to evaluate precisely the value of the ratio L(f,χ,m)/L(f,n) for a Hecke eigenform f. 相似文献
3.
M. Anoussis 《Advances in Mathematics》2004,188(2):425-443
Let G be a compact group, not necessarily abelian, let ? be its unitary dual, and for f∈L1(G), let fn?f∗?∗f denote n-fold convolution of f with itself and f? the Fourier transform of f. In this paper, we derive the following spectral radius formula
4.
V.M. Petrogradsky 《Journal of Pure and Applied Algebra》2007,208(3):1137-1158
We define the multiple zeta function of the free Abelian group Zd as
ζZd(s1,…,sd)=∑|Zd:H|<∞α1(H)−s1?αd(H)−sd, 相似文献
5.
Alain Escassut 《Topology and its Applications》2006,153(7):1152-1163
Let L be a field complete for a non-trivial ultrametric absolute value and let (A,‖⋅‖) be a commutative normed L-algebra with unity whose spectral semi-norm is ‖⋅‖si. Let Mult(A,‖⋅‖) be the set of continuous multiplicative semi-norms of A, let S be the Shilov boundary for (A,‖⋅‖si) and let ψ∈Mult(A,‖⋅‖si). Then ψ belongs to S if and only if for every neighborhood U of ψ in Mult(A,‖⋅‖), there exists θ∈U and g∈A satisfying ‖g‖si=θ(g) and . Suppose A is uniform, let f∈A and let Z(f)={?∈Mult(A,‖⋅‖)|?(f)=0}. Then f is a topological divisor of zero if and only if there exists ψ∈S such that ψ(f)=0. Suppose now A is complete. If f is not a divisor of zero, then it is a topological divisor of zero if and only if the ideal fA is not closed in A. Suppose A is ultrametric, complete and Noetherian. All topological divisors of zero are divisors of zero. This applies to affinoid algebras. Let A be a Krasner algebra H(D) without non-trivial idempotents: an element f∈H(D) is a topological divisor of zero if and only if fH(D) is not a closed ideal; moreover, H(D) is a principal ideal ring if and only if it has no topological divisors of zero but 0 (this new condition adds to the well-known set of equivalent conditions found in 1969). 相似文献
6.
Text
Let G be a finite cyclic group. Every sequence S over G can be written in the form S=(n1g)⋅…⋅(nlg) where g∈G and n1,…,nl∈[1,ord(g)], and the index ind(S) of S is defined to be the minimum of (n1+?+nl)/ord(g) over all possible g∈G such that 〈g〉=〈supp(S)〉. The problem regarding the index of sequences has been studied in a series of papers, and a main focus is to determine sequences of index 1. In the present paper, we show that if G is a cyclic of prime power order such that gcd(|G|,6)=1, then every minimal zero-sum sequence of length 4 has index 1.Video
For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=BC7josX_xVs. 相似文献7.
Guangshi Lü 《Journal of Number Theory》2009,129(11):2790-2800
Let λ(n) be the nth normalized Fourier coefficient of a holomorphic Hecke eigencuspform f(z) of even integral weight k for the full modular group. In this paper we are able to prove the following results.
- (i)
- For any ε>0, we have
8.
Tengiz Kopaliani 《Journal of Functional Analysis》2009,257(11):3541-3551
When Hardy-Littlewood maximal operator is bounded on Lp(⋅)(Rn) space we prove θ[Lp(⋅)(Rn),BMO(Rn)]=Lq(⋅)(Rn) where q(⋅)=p(⋅)/(1−θ) and θ[Lp(⋅)(Rn),H1(Rn)]=Lq(⋅)(Rn) where 1/q(⋅)=θ+(1−θ)/p(⋅). 相似文献
9.
Let G be a compact nonmetrizable topological group whose local weight b(G) has uncountable cofinality. Let H be an amenable locally compact group, A(G×H) the Fourier algebra of G×H, and UC2(G×H) the space of uniformly continuous functionals in VN(G×H)=A∗(G×H). We use weak factorization of operators in the group von Neumann algebra VN(G×H) to prove that there exist at least 2b(G)2 left ideals of dimensions at least 2b(G)2 in A(G×H)∗∗ and in UC2∗(G×H). We show that every nontrivial right ideal in A(G×H)∗∗ and in UC2∗(G×H) has dimension at least 2b(G)2. 相似文献
10.
Let be an affine R-monoid scheme. We prove that the category of dual functors (over the category of commutative R-algebras) of G-modules is equivalent to the category of dual functors of A∗-modules. We prove that G is invariant exact if and only if A∗=R×B∗ as R-algebras and the first projection A∗→R is the unit of A. If M is a dual functor of G-modules and wG?(1,0)∈R×B∗=A∗, we prove that MG=wG⋅M and M=wG⋅M⊕(1−wG)⋅M; hence, the Reynolds operator can be defined on M. 相似文献
11.
J.M. Calabuig E.A. Sánchez-Pérez 《Journal of Mathematical Analysis and Applications》2011,373(1):316-321
Let X be a Banach space and E an order continuous Banach function space over a finite measure μ. We prove that an operator T in the Köthe-Bochner space E(X) is a multiplication operator (by a function in L∞(μ)) if and only if the equality T(g〈f,x∗〉x)=g〈T(f),x∗〉x holds for every g∈L∞(μ), f∈E(X), x∈X and x∗∈X∗. 相似文献
12.
V. Blomer 《manuscripta mathematica》2005,117(2):111-133
Let f and g be two primitive (holomorphic or Maass) cusp forms of arbitrary level, character and infinity parameter by which we mean the weight in the holomorphic case and the spectral parameter in the Maass case. Let L(s,f × g) be the associated Rankin-Selberg L-function.If g is fixed and the infinity parameter f of f varies, then for s on the critical line, the subconvex estimate is any admissible value for the Ramanujan-Petersson-conjecture. 相似文献
13.
Najla A. Altwaijry 《Journal of Functional Analysis》2008,254(11):2866-2892
The Banach-Lie algebra L(A) of multiplication operators on the JB∗-triple A is introduced and it is shown that the hermitian part Lh(A) of L(A) is a unital GM-space the base of the dual cone in the dual GL-space ∗(Lh(A)) of which is affine isomorphic and weak∗-homeomorphic to the state space of L(A). In the case in which A is a JBW∗-triple, it is shown that tripotents u and v in A are orthogonal if and only if the corresponding multiplication operators in the unital GM-space Lh(A) satisfy
0?D(u,u)+D(v,v)?idA, 相似文献
14.
Mamoon A. Ahmed 《Journal of Mathematical Analysis and Applications》2010,364(2):498-507
Let (G,G+) be a quasi-lattice-ordered group with positive cone G+. Laca and Raeburn have shown that the universal C∗-algebra C∗(G,G+) introduced by Nica is a crossed product BG+α×G+ by a semigroup of endomorphisms. The goal of this paper is to extend some results for totally ordered abelian groups to the case of discrete lattice-ordered abelian groups. In particular given a hereditary subsemigroup H+ of G+ we introduce a closed ideal IH+ of the C∗-algebra BG+. We construct an approximate identity for this ideal and show that IH+ is extendibly α-invariant. It follows that there is an isomorphism between C∗-crossed products and B+(G/H)β×G+. This leads to our main result that B+(G/H)β×G+ is realized as an induced C∗-algebra . 相似文献
15.
Florin Nicolae 《Journal of Number Theory》2007,124(1):26-30
Let K/Q be a finite Galois extension with the Galois group G, let χ1,…,χr be the irreducible non-trivial characters of G, and let A be the C-algebra generated by the Artin L-functions L(s,χ1),…,L(s,χr). Let B be the subalgebra of A generated by the L-functions corresponding to induced characters of non-trivial one-dimensional characters of subgroups of G. We prove: (1) B is of Krull dimension r and has the same quotient field as A; (2) B=A iff G is M-group; (3) the integral closure of B in A equals A iff G is quasi-M-group. 相似文献
16.
Let E be a real normed linear space, K be a nonempty subset of E and be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., , and there exist x∗∈F(T) and a strictly increasing function , Φ(0)=0 such that for all x∈K, there exists j(x−x∗)∈J(x−x∗) such that
〈Tx−x∗,j(x−x∗)〉?‖x−x∗‖2−Φ(‖x−x∗‖). 相似文献
17.
Dongho Byeon 《Journal of Number Theory》2011,131(8):1513-1529
Let m be a positive integer and fm(x) be a polynomial of the form fm(x)=x2+x−m. We call a polynomial fm(x) a Rabinowitsch polynomial if for and consecutive integers x=x0,x0+1,…,x0+s−1, |fm(x)| is either 1 or prime. In this paper, we show that there are exactly 14 Rabinowitsch polynomials fm(x). 相似文献
18.
S.V. Ivanov 《Advances in Mathematics》2008,218(2):465-484
The Kurosh rank rK(H) of a subgroup H of a free product of groups Gα, α∈I, is defined accordingly to the classic Kurosh subgroup theorem as the number of free factors of H. We prove that if H1, H2 are subgroups of and H1, H2 have finite Kurosh rank, then , where , q∗ is the minimum of orders >2 of finite subgroups of groups Gα, α∈I, q∗:=∞ if there are no such subgroups, and if q∗=∞. In particular, if the factors Gα, α∈I, are torsion-free groups, then . 相似文献
19.
Nicholas J. Kuhn 《Advances in Mathematics》2007,216(1):387-442
Fix a prime p. Given a finite group G, let H∗(G) denote its mod p cohomology. In the early 1990s, Henn, Lannes, and Schwartz introduced two invariants d0(G) and d1(G) of H∗(G) viewed as a module over the mod p Steenrod algebra. They showed that, in a precise sense, H∗(G) is respectively detected and determined by Hd(CG(V)) for d?d0(G) and d?d1(G), with V running through the elementary abelian p-subgroups of G.The main goal of this paper is to study how to calculate these invariants. We find that a critical role is played by the image of the restriction of H∗(G) to H∗(C), where C is the maximal central elementary abelian p-subgroup of G. A measure of this is the top degree e(G) of the finite dimensional Hopf algebra H∗(C)⊗H∗(G)Fp, a number that tends to be quite easy to calculate.Our results are complete when G has a p-Sylow subgroup P in which every element of order p is central. Using the Benson-Carlson duality, we show that in this case, d0(G)=d0(P)=e(P), and a similar exact formula holds for d1. As a bonus, we learn that He(G)(P) contains nontrivial essential cohomology, reproving and sharpening a theorem of Adem and Karagueuzian.In general, we are able to show that d0(G)?max{e(CG(V))|V<G} if certain cases of Benson's Regularity Conjecture hold. In particular, this inequality holds for all groups such that the difference between the p-rank of G and the depth of H∗(G) is at most 2. When we look at examples with p=2, we learn that d0(G)?14 for all groups with 2-Sylow subgroup of order up to 64, with equality realized when G=SU(3,4).En route we study two objects of independent interest. If C is any central elementary abelian p-subgroup of G, then H∗(G) is an H∗(C)-comodule, and we prove that the subalgebra of H∗(C)-primitives is always Noetherian of Krull dimension equal to the p-rank of G minus the p-rank of C. If the depth of H∗(G) equals the rank of Z(G), we show that the depth essential cohomology of G is nonzero (reproving and extending a theorem of Green), and Cohen-Macauley in a certain sense, and prove related structural results. 相似文献
20.
Caishi Wang 《Journal of Mathematical Analysis and Applications》2007,329(2):913-921
Let δa be the Dirac delta function at a∈R and (E)⊂(L2)⊂∗(E) the canonical framework of white noise analysis over white noise space (E∗,μ), where E∗=S∗(R). For h∈H=L2(R) with h≠0, denote by Mh the operator of multiplication by Wh=〈⋅,h〉 in (L2). In this paper, we first show that Mh is δa-composable. Thus the delta function δa(Mh) makes sense as a generalized operator, i.e. a continuous linear operator from (E) to ∗(E). We then establish a formula showing an intimate connection between δa(Mh) as a generalized operator and δa(Wh) as a generalized functional. We also obtain the representation of δa(Mh) as a series of integral kernel operators. Finally we prove that δa(Mh) depends continuously on a∈R. 相似文献