Related papers: Mayer Transfer Operator Approach to Selberg Zeta F…

In this paper, we present two new representations of the alternating Zeta function. We show that for any s $\in$ C this function can be computed as a limit of a series of determinant. We then express these determinants as the expectation of…

Emil Artin defined a zeta function for algebraic curves over finite fields and made a conjecture about them analogous to the famous Riemann hypothesis. This and other conjectures about these zeta functions would come to be called the Weil…

A new definition for the Dirichlet beta function for positive integer arguments is discovered and presented for the first time. This redefinition of the Dirichlet beta function, based on the polygamma function for some special values,…

In this paper, a heuristic method to compute the Selberg zeta function for Hecke triangle groups, $G_q$ ($q>=3$) is described. The algorithm is based on the transfer operator method and an overview of the relevant background is given. We…

This note is about the spectral properties of transfer operators associated to smooth hyperbolic dynamics. In the first two sections (written in 2006), we state our new results relating such spectra with dynamical determinants, first…

We define generalised zeta functions associated to indefinite quadratic forms of signature (g-1,1) -- and more generally, to complex symmetric matrices whose imaginary part has signature (g-1,1) -- and we investigate their properties. These…

In recent years Lichtenbaum has conjectured a description for the special values of Hasse--Weil zeta functions in terms of ``Weil-\'etale cohomology''. In earlier papers we studied a class of foliated dynamical systems which had some…

In this paper we define a symmetric zeta function. We show that it can be analytically continued to a meromorphic function on $\mathbb{C}^3$ with only simple poles at some special hyperplanes. We also calculate the value of a multiple…

In this paper, we consider Hecke triangle groups $\Gamma_w$ for $w>2$ and associated infinite-volume orbifolds $\Gamma_w \backslash \mathbb{H}$. We show that the Selberg zeta function $Z_{\Gamma_w}(s)$ can be approximated for $s \in…

The transfer operator associated to a flow (continuous time dynamical system) is a one-parameter operator semigroup. We consider the operator-valued Laplace transform of this one-parameter semigroup. Estimates on the Laplace transform have…

A "quasiclassical" approximation to the quantum spectrum of the Schroedinger equation is obtained from the trace of a quasiclassical evolution operator for the "hydrodynamical" version of the theory, in which the dynamical evolution takes…

By building on former results and the cusp expansion algorithm, we construct strict transfer operator approaches for geometrically finite developable hyperbolic orbisurfaces of infinite area without cusps. Together with the cusp expansion…

In this paper,we develop a novel representation of the zeta function expressed as the limiting difference between two structured double sums. This approach leads to a new and elegant identity involving maximum functions and additive terms,…

It is well known that Euler experimentally discovered the functional equation of the Riemann zeta function. Indeed he detected the fundamental $s\mapsto 1-s$ invariance of $\zeta(s)$ by looking only at special values. In particular, via…

We initiate the study of spectral zeta functions $\zeta_{X}$ for finite and infinite graphs $X$, instead of the Ihara zeta function, with a perspective towards zeta functions from number theory and connections to hypergeometric functions.…

We show that the Ruelle zeta function of any smooth Axiom A flow with orientable stable/unstable spaces has a meromorphic continuation to the entire complex plane. The proof uses the meromorphic continuation result of [arXiv:1410.5516]…

We study Selberg zeta functions $Z(s,\sigma)$ associated to locally homogeneous vector bundles over the unit-sphere bundle of a complete odd-dimensional hyperbolic manifold of finite volume. We assume a certain condition on the fundamental…

We present the first example of the Selberg type zeta function for noncompact higher rank locally symmetric spaces. We study certain Selberg type zeta functions and Ruelle type zeta functions attached to the Hilbert modular group of a real…

It is known that the Selberg zeta function for the modular group has an expression in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. In the present paper, we generalize such a expression to…

In this note we introduce zeta functions and L-functions for discrete and faithful representations of surface groups in PSL(d, R), for d >= 3. These are natural generalizations of the wellknown classical Selberg zeta function and L-function…