# Transfer Operators, the Selberg Zeta Function and the Lewis-Zagier Theory of Period Functions / Dieter H. Mayer -- V. On the Calculation of Maass Cusp Forms

This paper generalizes Bass ’ work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The main theorems relate the zeta function to determin" Abstract - Cited by 11 (0 self) - Add to MetaCart

In the paper [KW2] we introduced a new type of Selberg zeta function for establishing a certain identity among the non-trivial zeroes of the Selberg zeta function and of the Riemann zeta function. We shall call this zeta function a higher Selberg zeta function. The purpose of this paper is to study the analytic properties of the higher Selberg zeta This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations.

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 This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations.

DETERMINANT EXPRESSION OF SELBERG ZETA FUNCTIONS (III) SHIN-YA KOYAMA (Communicated by William Adams) Abstract. We will prove that for PSL(2, R) and its cofinite subgroup, the Selberg zeta function is expressed by the determinant of the Laplacian.

## T1 - Turing’s Method for the Selberg Zeta-Function. AU - Booker, Andrew. AU - Platt, David J. PY - 2019/1/24. Y1 - 2019/1/24. N2 - In one of his final research papers, Alan Turing introduced a method to certify the completeness of a purported list of zeros of the Riemann zeta-function.

Köp boken An Approach to the Selberg Trace Formula via the Selberg Zeta-Function av Jurgen Fischer An Approach to the Selberg Trace Formula Via the Selberg Zeta-Function: 1253: Fischer, Jrgen: Amazon.se: Books. Selberg Zeta Functions and Transfer Operators: An Experimental Approach to Singular Perturbations: 2139: Fraczek: Amazon.se: Books. Pris: 339 kr. Häftad, 1987.

### 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.

DOI: 10.1215/S0012-7094-76 Zeta functions and complexities of a semiregular bipartite graph and its line graph. Iwao Sato. THE IHARA–SELBERG ZETA FUNCTION FOR PGL3 AND HECKE OPERATORS. Bass, H. (1992) The Ihara-Selberg Zeta Function of a Tree Lattice.

Selberg and Ruelle zeta functions for compact hyperbolic manifolds . V. Baladi, Dynamical zeta functions, arXiv:1602.05873. Relation to the volume of hyperbolic manifolds is discussed in
We initiate the study of Selberg zeta functions Z,χ for geometrically ﬁnite Fuch-sian groups and ﬁnite-dimensional representations χ with non-expanding cusp monodromy. We show that for all choices of (,χ), the Selberg zeta function Z,χ converges on some half-plane in C. In addition, under the assumption that admits a
In the paper [KW2] we introduced a new type of Selberg zeta function for establishing a certain identity among the non-trivial zeroes of the Selberg zeta function and of the Riemann zeta function.

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has been cited by the following article: TITLE: Non-Backtracking Random Walks and a Weighted Ihara’s Theorem. AUTHORS: Mark Kempton ICE Zeta functions, the Chowla-Selberg formula, and the Casimir effect EMILIOELIZALDE ICE/CSIC & IEEC, UAB, Barcelona MITP Workshop “Quantum Vacuum and Gravitation” THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE. HYMAN BASS. HYMAN BASS. Department of Mathematics, Columbia University, New York, NY 10027, USA. Search for more papers by this author.

The traces of powers of a Laplacian can be used to define the Selberg zeta function. The interest of this case was the analogy between the formula obtained, and the explicit formulae of prime number theory.

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### Inom matematiken är Selbergklassen en klass av Dirichletserier som verkar vara de essentiella egenskaperna satisfierade av de flesta L- och zetafunktioner. Ivić, Aleksandar (2013), The theory of Hardy's Z-function, Cambridge Tracts in

That the functions are entire and not only meromorphic is proved by a new method, identifying In this case the Selberg zeta function has zeros which come from non-trivial zeros of the Riemann zeta function. But they are not our objects of this study.

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### binary quadratic forms can be used to establish a connection between the transfer operator of the geodesic flow and the Selberg zeta function of the surface.

We consider geometrically finite We give an explicit formula for the second variation of the logarithm of the Selberg zeta function, Z(s), on Teichmüller space. We then use this formula to Sammanfattning: We give an explicit formula for the second variation of the logarithm of the Selberg zeta function, Z(s), on Teichmüller space. We then use this Pris: 336 kr. häftad, 1987.

## av A Kainberg · 2012 — Efter detta har satsen bevisats på både elementära sätt (Selberg & Erdõs, 1949) och med hjälp [Ford] K. Ford: Zero-free regions for the Riemann zeta function,.

In order to study the kernel on the imaginary axis we consider the equation i@ tW(it;x;y) = p M;xW(it;x;y) ; lim 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. This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic 1998-12-07 · In this context, the inverse of the Alexander polynomial of a knot plays the role of an Ihara-Selberg zeta function of a directed weighted graph, counting with weights cycles of random walk on a 1-string link whose closure is the knot in question. 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.

Selberg Zeta The Selberg zeta function is decomposed into a canonical product over its zeros in analogy with the.