2. The Selberg zeta function 1 3. Reduction theory 2 4. The transfer operator L s 4 5. Selberg zeta functions and transfer operators 7 6. A dynamical point of view on Z Γ 0 10 References 15 1. Introduction In this paper we are interested in the Selberg zeta functions for mod-ular groups. We ﬁrst deﬁne it from a purely algebraical point of

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The selberg trace formula and the riemann zeta function. Duke Mathematical Journal, 43(3), 441-482. https://doi.org/10.1215/S0012-7094-76-04338-6 We study the asymptotic behavior of zeros of the Selberg zeta function for the congruence subgroup Γ 0 (4) as a function of a one-parameter family of characters tending to the trivial character. The motivation for the study comes from observations based on numerical computations.

Selberg zeta function

Department of Mathematics, Columbia University, New York, NY 10027, USA. Search for more papers by this author. https://doi.org/10.1142/S0129167X92000357 Cited by: 171. On Epstein's Zeta-function. S. Chowla; A. Selberg. Journal für die reine und angewandte Mathematik (1967) Volume: 227, page 86-110.

The Selberg zeta-function was introduced by Template:Harvs.It is analogous to the famous Riemann zeta function ⁡ = ∏ ∈ − − where is the set of prime numbers. The Selberg zeta-function uses the lengths of simple closed geodesics instead of the primes numbers.

arXiv:1506.04672v1 [math.SP] 15 Jun 2015 Ruelle and Selberg zeta functions for non-unitary twists Polyxeni Spilioti Abstract. In this paper, we study the Selberg and Ruelle zeta f 2013-02-01 · Moreover, introducing a “poly-Selberg zeta function” Z Γ (m) (s) by a certain Euler product (which is regarded as another generalization of the Selberg zeta function), we show that Z Γ, r (s) can be expressed as a product and quotient of Z Γ (m) (s) (Theorem 4.11). This is nothing but the Euler product expression of Z Γ, r (s). In the present paper, we study the growth of the Selberg zeta function for the modular group in the critical strip.

We study the asymptotic behavior of zeros of the Selberg zeta function for the congruence subgroup Γ 0 (4) as a function of a one-parameter family of characters tending to the trivial character. The motivation for the study comes from observations based on numerical computations.

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Selberg Zeta function. Geodesic and Anosov flows. Applications. Prime Number Theorem. The Riemann Abstract.
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The colored Jones polynomial then counts with weights families of ``self-avoiding'' cycles of random Bass, H. (1992) The Ihara-Selberg Zeta Function of a Tree Lattice. International Journal of Mathematics, 3, 717-797. http://dx.doi.org/10.1142/S0129167X92000357 .

All of related to Selberg's zeta function for the modular surfaceE/PSL (2, Z). In§4we consider multivariable statistical mechanics zeta functions for one-dimensional Apr 30, 2017 The Riemann zeta function is connected to the prime numbers distribution, in particular Riemann argued that all of its non trivial zerosIn this case, It is closely related to the Epstein zeta function.
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Keywords Selberg zeta function non-compact surface conﬁguration of zeros PACS 11M36 37C30 1 Introduction The Selberg zeta function Z X associated to a compact Riemann surface X with negative Euler characteristic and without boundary is a well known and much studied complex function. It is a

In mathematics, the Selberg conjecture, named after Atle Selberg, is a theorem about the density of zeros of the Riemann zeta function ζ(1/2 + it). It is known that the function has infinitely many zeroes on this line in the complex plane: the point at issue is how densely they are clustered. The Selberg zeta function controls the asymptotics of prime geodesics via the prime geodesic theorem in direct analogy to how the Riemann zeta function controls the asymptotics of prime numbers via the prime number theorem. Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then the Selberg zeta function is defined as Z(s)=product_({p})product_(k=0)^infty[1-e^(-tau(p)(s+k))], for s>1.

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Pankaj Vishe: The Zeta function and Prime number theorem. 16 On the distribution of zeros of the derivative of the Selberg zeta function. 16.

For example Determinant of Laplacian acting on various tensor fields on the Riemman surface can be written in terms of Selberg zeta function. Hejhal, D. A. (1976). The selberg trace formula and the riemann zeta function. Duke Mathematical Journal, 43(3), 441-482. https://doi.org/10.1215/S0012-7094-76-04338-6 We study the asymptotic behavior of zeros of the Selberg zeta function for the congruence subgroup Γ 0 (4) as a function of a one-parameter family of characters tending to the trivial character.

Continued Fractions and the Selberg zeta function of the modular curve (Ayberk Zeytin - Galatasaray University). turkmath.org. Bilkent Üniversitesi ODTÜ-Bilkent

The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained. September 1976 The Selberg trace formula and the Riemann zeta function.

HYMAN BASS. HYMAN BASS. Department of Mathematics, Columbia University, New York, NY 10027, USA. Search for more papers by this author. https://doi.org/10.1142/S0129167X92000357 Cited by: 171. On Epstein's Zeta-function. S. Chowla; A. Selberg. Journal für die reine und angewandte Mathematik (1967) Volume: 227, page 86-110.