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1.
We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of . Let S be a set of finite places of K, such that the sum is convergent. Then π is uniquely determined by the collection of the local components finite} of π. Combining this theorem with base change, it is possible to consider sets S of positive density, having appropriate splitting behavior with respect to a solvable extension L of K, and where π is determined up to twisting by a character of the Galois group of L over K.  相似文献   

2.
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:
Gθf1Es,θf2〉=Hf1,f2〉⋅Lstd(f1,s).  相似文献   

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We explain how the Bloch-Kato conjecture leads us to the following conclusion: a large prime dividing a critical value of the L-function of a classical Hecke eigenform f of level 1, should often also divide certain ratios of critical values for the standard L-function of a related genus two (and in general vector-valued) Hecke eigenform F. The relation between f and F (Harder?s conjecture in the vector-valued case) is a congruence involving Hecke eigenvalues, modulo the large prime. In the scalar-valued case we prove the divisibility, subject to weak conditions. In two instances in the vector-valued case, we confirm the divisibility using elaborate computations involving special differential operators. These computations do not depend for their validity on any unproved conjecture.  相似文献   

5.
Marvin Knopp showed that entire automorphic integrals with rational period functions satisfy a Hecke correspondence theorem, provided the rational period functions have poles only at 0 or ∞. For other automorphic integrals the corresponding Dirichlet series has a functional equation with a remainder term that arises from the nonzero poles of the rational period function. In this paper we prove a Hecke correspondence theorem for a class of automorphic integrals with rational period functions on the Hecke groups. We restrict our attention to automorphic integrals of weight that is twice an odd integer and to rational period functions that satisfy a symmetry property we call “Hecke-symmetry.” Each remainder term satisfies two relations (the second of which is new in this paper) corresponding to the two relations for the rational period function.  相似文献   

6.
A decomposition theorem for Jacobi forms   总被引:1,自引:0,他引:1  
  相似文献   

7.
We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm. These relations suffice, as we shall demonstrate with a few examples, to write down enough relations in Bloch's integral higher Chow group CH2(F,3) for certain number fields F to detect torsion cycles. Using the regulator map to Deligne cohomology, one can check the non-triviality of the torsion cycles thus obtained. Using this combination of methods, we obtain explicit higher Chow cycles generating the integral motivic cohomology groups of some number fields.  相似文献   

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9.
Summary Letf be a real-valued function with period 1 satisfying some regularity conditions. It will be proved that, for any 1,..., d > 1, the distribution of on the probability space ([0, 1],dt) converges to a normal distribution whose covariance is given by algebraic relations among the i 's. This generalizes the classical work by M. Kac and refines the characterization off to have a degenerate limit. It also shows that the limit law of is in most cases a Cauchy distribution.  相似文献   

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We establish a mean square estimate on the weight aspect for symmetric square L-functions at every point on the critical line.Received: 15 February 2002  相似文献   

12.
In a previous paper [X. Hou, K.H. Leung, Q. Xiang, A generalization of an addition theorem of Kneser, J. Number Theory 97 (2002) 1-9], the following result was established: let EK be fields such that the algebraic closure of E in K is separable over E. Let A,B be E-subspaces of K such that 0<dimEA< and 0<dimEB<. Then dimEAB?dimEA+dimEB-dimEH(AB), where AB is the E-space generated by {ab:aA,bB} and H(AB)={xK:xABAB}. The separability assumption was essential in the proof of this result. However, even without the separability assumption, no counterexample is known. The present paper shows that no counterexample can be found if dimEA?5.  相似文献   

13.
We close a gap in Humbert’s classical calculation of the volume of the quotient of three-dimensional hyperbolic space by SL2 over the ring of integers of an imaginary quadratic number field.  相似文献   

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In this paper we study the construction and non-vanishing of cuspidal modular forms of weight m?3 for arbitrary Fuchsian groups of the first kind. We give a spanning set for the space of cuspidal modular forms Sm(Γ) of weight m?3 in a uniform way which does not depend on the fact that Γ has cusps or not.  相似文献   

16.
partially supported by NSF grant #DMS-8919696  相似文献   

17.
We prove an explicit formula for the central values of certain Rankin L-functions. These L-functions are the L-functions attached to Hilbert newforms over a totally real field F, twisted by unitary Hecke characters of a totally imaginary quadratic extension of F. This formula generalizes our former result on L-functions twisted by finite CM characters.  相似文献   

18.
In this paper we prove a theorem on |A|k,k≥1|A|k,k1, summability factors for an infinite series by replacing a weighted mean matrix with a triangular matrix.  相似文献   

19.
We associate a set of half integral weight forms to an integral weight newform of odd level. We prove an explicit identity relating the central values of the twist L-functions of the newform to the Fourier coefficients of the half integral weight forms.  相似文献   

20.
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