共查询到20条相似文献,搜索用时 31 毫秒
1.
We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface under deformation of the surface. Our calculations indicate that if the Teichmüller space of is not trivial, then each cusp form has a set of deformations under which either the cusp form remains a cusp form or else it dissolves into a resonance whose constant term is uniformly a factor of smaller than a typical Fourier coefficient of the form. We give explicit examples of those deformations in several cases.
2.
QU Yan School of Mathematics Sh ong University Jinan China Institut lie Cartan Universit Nancy B.P. F- France 《中国科学 数学(英文版)》2010,(1)
Let f be a Maass eigenform that is a new form of level N on Γ0(N),with Laplace eigenvalue 1/4 + νf2 . Then,all its Fourier coefficients {λf(n)}∞n=1 are real,and we may normalize so that λf (1) = 1. It is proved,in this paper,that the first sign change in the sequence {λf(n)}n∞=1 occurs at some n satisfying n《{(3+|νf|2)N }1/2-δ and (n,N)=1. This generalizes the previous results for holomorphic Hecke eigenforms. 相似文献
3.
Hengcai TANG 《Frontiers of Mathematics in China》2013,8(4):923-932
Let f(z) be a Hecke-Maass cusp form for SL 2(?), and let L(s, f) be the corresponding automorphic L-function associated to f. For sufficiently large T, let N(σ, T) be the number of zeros ρ = β +iγ of L(s, f) with |γ| ? T, β ? σ, the zeros being counted according to multiplicity. In this paper, we get that for 3/4 ? σ ? 1 ? ?, there exists a constant C = C(?) such that N(σ,T) ? T 2(1?σ)/σ(logT) C , which improves the previous results. 相似文献
4.
We study the exponential sums involving l:burmr coeffcients ot Maass forms and exponential functions of the form e(anZ), where 0 ≠ α∈R and 0 〈 β 〈 1. An asymptotic formula is proved for the nonlinear exponential sum ∑x〈n≤2x λg(n)e(αnβ), when β = 1/2 and |α| is close to 2√ q C Z+, where Ag(n) is the normalized n-th Fourier coefficient of a Maass cusp form for SL2 (Z). The similar natures of the divisor function 7(n) and the representation function r(n) in the circle problem in nonlinear exponential sums of the above type are also studied. 相似文献
5.
Recently, K. Bringmann, P. Guerzhoy, Z. Kent and K. Ono studied the connection between Eichler integrals and the holomorphic parts of harmonic weak Maass forms on the full modular group. In this article, we extend their result to more general groups, namely, H-groups by employing the theory of supplementary functions introduced and developed by M.I. Knopp and S.Y. Husseini. In particular, we show that the set of Eichler integrals, which have polynomial period functions, is the same as the set of holomorphic parts of harmonic weak Maass forms of which the non-holomorphic parts are certain period integrals of cusp forms. From this we deduce relations among period functions for harmonic weak Maass forms. 相似文献
6.
Let F be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms
forU (1, 1)(F), building on previous work onSL
2(F). This theory is analogous to the results of Casselman forGL
2(F) and Jacquet, Piatetski-Shapiro, and Shalika forGL
n(F). To a representation π ofU(1, 1)(F), we attach an integer c(π) called the conductor of π, which depends only on theL-packet π containing π. A newform is a vector in π which is essentially fixed by a congruence subgroup of level c(π). We show
that our newforms are always test vectors for some standard Whittaker functionals, and, in doing so, we give various explicit
formulae for newforms. 相似文献
7.
Let {øj(z) : j ≥ 1} be an orthonormal basis of Hecke-Maass cusp forms with Laplace eigenvalue 1/4 + tj2. For each øj(z), we have the automorphic L-function L(s, sym2øj) which is called the symmetric square L-function associated to øj. In this paper, the average estimate of L(1/2, sym2øj) is considered, i.e., for sufficiently large T, the asymptotic formula
is established, where αj is a certain fixed weight function and P(x) is a polynomial of degree 1. 相似文献
8.
9.
In this article we establish the analogue of a theorem of Kuznetsov (theorem 6 of [3]) in the case of 3-dimensional hyperbolic
space. We also consider a generalization of this result for higher dimensional hyperbolic spaces and discuss the relevant
ingredients of a proof.
Dedicated to the memory of Professor K G Ramanathan 相似文献
10.
Liqun HU 《Frontiers of Mathematics in China》2015,10(5):1101
For the normalized Fourier coefficients of Maass cusp forms λ(n) and the normalized Fourier coefficients of holomorphic cusp forms a(n), we give the bound of ∑ m 1 2 + m 2 2 + m 3 2 ≤ x λ ( m 1 2 + m 2 2 + m 3 2 ) Λ ( m 1 2 + m 2 2 + m 3 2 ) and ∑ m 1 2 + m 2 2 + m 3 2 ≤ x a ( m 1 2 + m 2 2 + m 3 2 ) Λ ( m 1 2 + m 2 2 + m 3 2 ) . 相似文献
11.
12.
Toshiro Watanabe 《Transactions of the American Mathematical Society》2007,359(6):2851-2879
The relation between the upper and lower asymptotic estimates of the density and the fractal dimensions on the sphere of the spectral measure for a multivariate stable distribution is discussed. In particular, the problem and the conjecture on the asymptotic estimates of multivariate stable densities in the work of Pruitt and Taylor in 1969 are solved. The proper asymptotic orders of the stable densities in the case where the spectral measure is absolutely continuous on the sphere, or discrete with the support being a finite set, or a mixture of such cases are obtained. Those results are applied to the moment of the last exit time from a ball and the Spitzer type limit theorem involving capacity for a multi-dimensional transient stable process.
13.
Yu. N. Lin'kov 《Journal of Mathematical Sciences》1991,53(1):49-55
For families of probability measures (P
, )) generated by semimartingales, we consider the local density)(y, )=
t
(y, ))
t0 of a, measureP
y
with respect to the measureP
whose logarithm is the difference of a local martingale and a positive predictable increasing locally bounded process. Conditions are obtained under which the relations
and
hold, wherey
t
depends in some way ont, while
t
ast . Applications of these relations are exhibited and an example is given when the hypotheses of the theorems proved can be verified.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 48–55, 1986. 相似文献
14.
Summary An asymptotic formula (as t ) is derived for the density of the first-exit time of the Brownian motion over certain upper class functions. This result is applied to the study of the performance of tests of power one as the drift goes to zero.This work has been supported by the Deutsche Forschungsgemeinschaft 相似文献
15.
Asymptotic expansions of posterior expectations,distributions and densities for stochastic processes
Martin Crowder 《Annals of the Institute of Statistical Mathematics》1988,40(2):297-309
Asymptotic expansions are derived for Bayesian posterior expectations, distribution functions and density functions. The observations constitute a general stochastic process in discrete or continuous time. 相似文献
16.
17.
18.
Let G be a split adjoint semisimple group over
and
a maximal compact subgroup. We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp forms
on congruence quotients of
. This proves a conjecture of Sarnak for
-split groups, previously known only for the case G = PGL(n). The key idea amounts to a new type of simple trace formula.
Received: April 2005 Revision: June 2006 Accepted: October 2006 相似文献
19.
In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a domain Ω in a given complete
(not compact a priori) Riemannian manifold (M,g). For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general
metric way, interesting for itself. As applications, we prove that if the Ricci curvature of (M,g) is bounded below Ric
g
≥−(n−1)a
2, a≥0, then there exist constants A
n
>0,B
n
>0 only depending on the dimension, such that
where λ
k
(Ω) (k∈ℕ*) denotes the k-th eigenvalue of the Neumann problem on any bounded domain Ω⊂M of volume V=Vol (Ω,g). Furthermore, this upper bound is clearly in agreement with the Weyl law. As a corollary, we get also an estimate which
is analogous to Buser’s upper bounds of the spectrum of a compact Riemannian manifold with lower bound on the Ricci curvature.
相似文献
20.
本文讨论了滑动和过程的Spitzer和Baum-Katz律的精确渐近,其中{ξ,ξi-∞相似文献