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.
The first paper is motivated by a conjecture of Patterson on the Selberg zeta function of Kleinian groups. We consider geometrically finite hyperbolic cylinders
This is the first example of the universal zeta-function of order 2. To prove this result we obtain the universality theorem for a wide class of generalized Dirichlet series. 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. DETERMINANT EXPRESSION OF SELBERG ZETA FUNCTIONS (III) SHIN-YA KOYAMA (Communicated by William Adams) Abstract.
Journal of Number Theory, 156, This method consists to approximate the exact solution through a linear combination of trial functions satisfying exactly the governing differential equation. The final chapter, on function spaces and harmonic analysis, is deliberately Selberg Zeta Functions and Transfer Operators - An Experimental Approach to 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 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,. Inom matematiken är Dedekinds zetafunktion av en algebraisk talkropp K, baserad på material från engelskspråkiga Wikipedia, Dedekind zeta function, 25 maj 2013. L-funktioner av Heckekaraktärer · Automorfisk L-funktion · Selbergklass.
The main theorems relate the zeta function to determin" Abstract - Cited by 11 (0 self) - Add to MetaCart On Epstein's Zeta-function. S. Chowla; A. Selberg. Journal für die reine und angewandte Mathematik (1967) Volume: 227, page 86-110; ISSN: 0075-4102; 1435-5345/e Abstract.
Higher Selberg Zeta Functions Higher Selberg Zeta Functions Kurokawa, Nobushige; Wakayama, Masato 2004-04-07 00:00:00 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.
2020-09-15 2011-11-30 James G. Huard, Pierre Kaplan, Kenneth S. Williams, The Chowla-Selberg formula for genera André Weil, La cyclotomie jadis et naguère Steven Arno, The imaginary quadratic fields of class number 4 Selberg Zeta Function 443 then Φ(t) admits a Mellίn transform JίΦ(s) in the vertical strip — i 0 < Res < — j 0,]1dt. (2.12) A standard problem is how to continue JίΦ{s) analytically to a wider strip.
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 determine the asymptotic behavior as Rs→ ∞ of the second variation. As a consequence, for m∈ N, we obtain the complete expansion in m of the curvature of the vector bundle H(Xt, Kt) → t∈ T of holomorphic m-differentials over the
International Journal of Mathematics, 3, 717-797. On Epstein's Zeta-function.
2020-09-15
2011-11-30
James G. Huard, Pierre Kaplan, Kenneth S. Williams, The Chowla-Selberg formula for genera André Weil, La cyclotomie jadis et naguère Steven Arno, The imaginary quadratic fields of class number 4
Selberg Zeta Function 443 then Φ(t) admits a Mellίn transform JίΦ(s) in the vertical strip — i 0 < Res < — j 0,]1dt. (2.12) A standard problem is how to continue JίΦ{s) analytically to a wider strip. Since-JiΦ{-s) = ] Φil/ήf-1 dr, (2.13)this problem has a left-right symmetry in 5, hence we may restrict the problem to
2. The Selberg zeta function 1 3. Reduction theory 2 4.
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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.
Amer. Math.
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The final chapter, on function spaces and harmonic analysis, is deliberately Selberg Zeta Functions and Transfer Operators - An Experimental Approach to
April 2021 Anke Pohl (U Bremen) Twisted SZF April 20211/18. Setup: geometrically nite hyperbolic surfaces nH IH hyperbolic plane Selberg zeta function and relative analytic torsion for hyperbolic odd-dimensional orbifolds Dissertation zur Erlangung des Doktorgrades (Dr.
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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
Department of Mathematics, Columbia University, New York, NY 10027, USA. Search for more papers by this author.
There are analogous functions arising in other fields such as. Selberg's zeta function of a Riemann surface, Ihara's zeta function of a finite connected graph. All of
A lighter account appears in [28]. 2.1 De nition: Hyperbolic geometry and closed geodesics 2 The Selberg zeta function for lengths of closed geodesics of surfaces of constant negative curvature; and 3 The Ruelle zeta function for periods of closed orbits of geodesic and Anosov ows. In particular, the Ruelle zeta function generalises the Selberg zeta function. The general philosophy 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 determine the asymptotic behavior as Rs→ ∞ of the second variation. 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.
Areas in which the theory has not Theta and Selberg Zeta Function Ulrich Bunke June 22, 2015 Abstract Contents 1 The Theta function 1 2 Hyperbolic space 5 3 The Selberg Trace Formula 8 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 Selberg zeta function and hyperbolic eisenstein series @article{Falliero2017SelbergZF, title={Selberg zeta function and hyperbolic eisenstein series}, author={Th'erese Falliero}, journal={arXiv: Spectral Theory}, year={2017} } 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 Selberg zeta-function. Selberg Zeta Functions and Transfer Operators An Experimental Approach to Singular Perturbations / by Markus Szymon Fraczek. Fraczek, Markus Szymon. (författare) SpringerLink (Online service) ISBN 9783319512969 Publicerad: Cham : Springer International Publishing : 2017 2001-10-01 Bass, H. (1992) The Ihara-Selberg Zeta Function of a Tree Lattice.