共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we study the Ruelle zeta function and the Selberg zeta functions attached to the fundamental representations
for real hyperbolic manifolds with cusps. In particular, we show that they have meromorphic extensions to
\mathbbC{\mathbb{C}} and satisfy functional equations. We also derive the order of the singularity of the Ruelle zeta function at the origin.
To prove these results, we completely analyze the weighted unipotent orbital integrals on the geometric side of the Selberg
trace formula when test functions are defined for the fundamental representations. 相似文献
2.
We will establish a theorem concerning value distribution of L‐functions in the Selberg class, which shows how an L‐function and a meromorphic function are uniquely determined by their c‐values and which, as a consequence, proves a result on the uniqueness of the Riemann zeta function. The results in this paper also extend the corresponding ones in Li 6 . 相似文献
3.
Daniel Bump Alexander Pekker 《Proceedings of the American Mathematical Society》2002,130(12):3473-3481
We compute the dimension of the space of theta functions of a given type using a variant of the Selberg trace formula.
4.
Makoto Minamide 《Monatshefte für Mathematik》2010,86(1):187-193
In this article, we study the zero-free region of the derivative of Selberg zeta functions associated with compact Riemann
surfaces and three-dimensional compact hyperbolic spaces. We obtain the zero-free region with respect to the left of the critical
line of each Selberg zeta function. This is an improvement of Wenzhi Luo’s zero-free region theorem for compact Riemann surfaces. 相似文献
5.
Yasufumi Hashimoto 《Journal of Number Theory》2007,122(2):324-335
In [P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982) 229-247], it was proved that the Selberg zeta function for SL2(Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms. The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg zeta functions for congruence subgroups of SL2(Z). As applications, we study the Brun-Titchmarsh type prime geodesic theorem and the asymptotic formula of the sum of the class number. 相似文献
6.
Polyxeni Spilioti 《Annals of Global Analysis and Geometry》2018,53(2):151-203
In this paper we study the dynamical zeta functions of Ruelle and Selberg associated with the geodesic flow of a compact hyperbolic odd-dimensional manifold. These are functions of a complex variable s in some right half-plane of \(\mathbb {C}\). Using the Selberg trace formula for arbitrary finite dimensional representations of the fundamental group of the manifold, we establish the meromorphic continuation of the dynamical zeta functions to the whole complex plane. We explicitly describe the singularities of the Selberg zeta function in terms of the spectrum of certain twisted Laplace and Dirac operators. 相似文献
7.
Makoto Minamide 《Monatshefte für Mathematik》2010,160(2):187-193
In this article, we study the zero-free region of the derivative of Selberg zeta functions associated with compact Riemann surfaces and three-dimensional compact hyperbolic spaces. We obtain the zero-free region with respect to the left of the critical line of each Selberg zeta function. This is an improvement of Wenzhi Luo’s zero-free region theorem for compact Riemann surfaces. 相似文献
8.
We calculate the wave kernels for the classical rank-one symmetric spaces. The result is employed in order to provide a meromorphic extension of the theta function of an even-dimensional compact locally symmetric space of non-compact type. Moreover we give a short derivation of the Selberg trace formula. We discuss the relation between the right hand side of the functional equation of the Selberg zeta function, the Plancherel measure, Weyl's dimension formula and the wave kernel on the non-compact symmetric space and on its compact dual in an explicit manner.The first two authors were supported by the Sonderforschungsbereich 288 Differentialgeometrie und Quantenphysik founded by the Deutsche Forschungsgemeinschaft. 相似文献
9.
The Ramanujan Journal - The Landau–Selberg–Delange method gives an asymptotic formula for the partial sums of a multiplicative function f whose prime values are $$\alpha $$ on average.... 相似文献
10.
We prove that the explicit formula in a symmetric case for a triple (Z,
[(Z)\tilde]\tilde{Z}
, Φ) in Jorgenson-Lang’s fundamental class of functions holds for a larger class of (not necessarily differentiable or even
continuous) test functions. As one of the most important applications, we show that the Selberg trace formula for a strictly
hyperbolic cocompact Fuchsian group Γ is valid for a larger class of test functions. Further applications to growth estimates
for the logarithmic derivative of the Selberg zeta function are considered. 相似文献
11.
Donggeng Gong 《manuscripta mathematica》1995,86(1):435-454
We define ζ-determinant andL
2-analytic torsion functions for a Riemann surface of finite volume. We use the Selberg trace formula to express these determinant
and torsion functions in terms of four Zeta functions which are related to the structure of discrete groups. A new invariant
is also obtained. 相似文献
12.
Some observations on the statistical independence and the distribution of zeros in the selberg class
Fabrizio Zanello 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):211-223
In this paper we prove four theorems on theL-function of the Selberg Class, extending some results of Selberg. Bombieri-Hejhal and Bombieri-Perelli, shown for a rather
similar class of Dirichlet series.
Today these theorems cannot yet be proven unconditionally, but still require some strong hypotheses, for both classes ofL-functions. 相似文献
13.
D. A. Popov 《Functional Analysis and Its Applications》2012,46(2):133-146
Let the standard Riemannian metric of constant curvature K = −1 be given on a compact Riemannian surface of genus g > 1. Under this condition, for a class of strictly hyperbolic Fuchsian groups, we obtain an explicit expression for the spectral
counting function of the Laplace operator in the form of a series over the zeros of the Selberg zeta function. 相似文献
14.
15.
Using the theory of Macdonald polynomials, a number of q-integrals of Selberg type are proved.
2000 Mathematics Subject Classification: Primary—33D05, 33D52, 33D60 相似文献
16.
Selberg type Jackson integrals satisfy q-difference equations of Birkhoff type (generally called q Knizhnik Zamolodchikov equations). In one variable case, these equation are explicitly derived in matrix form of Gauss decomposition, by limit procedure q→0 from the connection matrices, by solving Riemann-Hilbert problem. The latter are evaluated from the asymptotic behaviours of Jackson integrals and the connection formulas given in our previous paper. 相似文献
17.
We prove that the explicit formula in a symmetric case for a triple (Z,
, Φ) in Jorgenson-Lang’s fundamental class of functions holds for a larger class of (not necessarily differentiable or even
continuous) test functions. As one of the most important applications, we show that the Selberg trace formula for a strictly
hyperbolic cocompact Fuchsian group Γ is valid for a larger class of test functions. Further applications to growth estimates
for the logarithmic derivative of the Selberg zeta function are considered. 相似文献
18.
The ChowlaSelberg formula is applied in approximatinga given Epstein zeta function. Partial sums of the series derivefrom the ChowlaSelberg formula, and although these partialsums satisfy a functional equation, as does an Epstein zetafunction, they do not possess an Euler product. What we callpartial sums throughout this paper may be considered as specialcases concerning a more general function satisfying a functionalequation only. In this article we study the distribution ofzeros of the function. We show that in any strip containingthe critical line, all but finitely many zeros of the functionare simple and on the critical line. For many Epstein zeta functionswe show that all but finitely many non-trivial zeros of partialsums in the ChowlaSelberg formula are simple and on thecritical line. 2000 Mathematics Subject Classification 11M26. 相似文献
19.
A. Perelli 《Milan Journal of Mathematics》2010,78(1):117-134
This is a survey of joint work with Jerzy Kaczorowski about non-linear twists of L-functions. We present the theory of non-linear twists in the general framework of the Selberg class of L-functions. Applications, mainly to the classification of the Selberg class, are also described. 相似文献
20.
Giovanni Coppola Maurizio Laporta 《Proceedings of the Steklov Institute of Mathematics》2017,299(1):56-77
The weighted Selberg integral is a discrete mean-square that generalizes the classical Selberg integral of primes to an arithmetic function f, whose values in a short interval are suitably attached to a weight function. We give conditions on f and select a particular class of weights in order to investigate non-trivial bounds of weighted Selberg integrals of both f and f * μ. In particular, we discuss the cases of the symmetry integral and the modified Selberg integral, the latter involving the Cesaro weight. We also prove some side results when f is a divisor function. 相似文献