# Abstract. In 1975 S. M. Voronin proved that the Riemann zeta-function is universal in the strip . We prove that the Selberg zeta-function for the modular group is universal in the strip . This is the first example of the universal zeta-function of order 2.

Pris: 336 kr. häftad, 1987. Skickas inom 5-9 vardagar. Köp boken An Approach to the Selberg Trace Formula via the Selberg Zeta-Function av Jurgen Fischer

It is analogous to the famous Riemann zeta function. ζ ( s ) = ∏ p ∈ P 1 1 − p − s {\displaystyle \zeta (s)=\prod _ {p\in \mathbb {P} } {\frac {1} {1-p^ {-s}}}} where. P {\displaystyle \mathbb {P} } is the set of prime numbers. 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.

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. For a geometrically finite hyperbolic surface X the Selberg zeta function Z X (s) was introduced in §2.5.

Reduction theory 2 4.

## Finaly, in chapter 4, the Riemann zeta-function and the Riemann hypothesis is considered. Sats 3.15 (Selberg): För lika med I nedanstående sats

Sök bland 100181 avhandlingar från svenska högskolor och universitet på Avhandlingar.se. It is closely related to the Epstein zeta function.

### The functional determinant of an eigenvalue sequence, as defined by zeta regularization, can be simply evaluated by quadratures. We apply this procedure to the Selberg trace formula for a compact Riemann surface to find a factorization of the Selberg zeta function into two functional determinants, respectively related to the Laplacian on the compact surface itself, and on the sphere.

In the present paper, we study the growth of the Selberg zeta function for the modular group in the critical strip. 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. We will also give an explicit calculation in case of congruence subgroups, and deduce Generalised Selberg zeta functions and a conjectural Lefschetz formula Anton Deitmar S. Friedberg et al: Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory. Proceedings of Symposia in Pure Mathematics, Volume: 75, 177- 190 (2006). Abstract.

Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant - Volume 33 Issue 1 Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Voros, A.: Spectral Functions, Special Functions and the Selberg Zeta Function. Commun. Math. Phys. 110, 439–465, 1987.

Mass of neutron

Journal für die reine und angewandte Mathematik (1967) Volume: 227, page 86-110. ISSN: 0075-4102; 1435-5345/e.

We consider geometrically finite hyperbolic cylinders
av J Peetre · 2009 — seminar on the zeta-functionen where, among other things, Selberg has 58This is the famous Minaskshisundaram-Pleijel zeta function [?].

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### The Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the

We then use this Pris: 336 kr. häftad, 1987. Skickas inom 5-9 vardagar.

## SELBERG'S ZETA-FUNCIION AND THE ASYMPTOTIC BEHP' -)R OF EIGENVALUES OF THE LAPLACE OPERATOR BY BURTON RANDOL ABsrRAcr. Much of that part of the theory of the Riemann zeta-function based on the Riemann hypothesis carries over to zeta-functions of Selberg's type, and in this way one can get asymptotic information about various eigenvalue problems.

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.

L-funktioner av Heckekaraktärer · Automorfisk L-funktion · Selbergklass. Pankaj Vishe: The Zeta function and Prime number theorem. 16 On the distribution of zeros of the derivative of the Selberg zeta function.