Cover of: Dynamical, spectral, and arithmetic zeta functions | AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions (1999 San Antonio, Tex.)

Dynamical, spectral, and arithmetic zeta functions

AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions, January 15-16, 1999, San Antonio, Texas
  • 195 Pages
  • 0.19 MB
  • 9922 Downloads
  • English
by
American Mathematical Society , Providence, R.I
Functions, Zeta -- Congr
StatementMichel L. Lapidus, Machiel Van Frankenhuysen, editors
GenreCongresses
SeriesContemporary mathematics -- 290, Contemporary mathematics (American Mathematical Society) -- v. 290
ContributionsLapidus, Michel L. 1956-, Van Frankenhuysen, Machiel, 1967-
Classifications
LC ClassificationsQA351 .A73 1999
The Physical Object
Paginationx, 195 p. :
ID Numbers
Open LibraryOL17030815M
ISBN 100821820796
LC Control Number2001053944

and arithmetic zeta functions book The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function.

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Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. Get this from a library.

Dynamical, spectral, and arithmetic zeta functions: AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions, January, San Antonio, Texas. [Michel L Lapidus; Machiel Van Frankenhuysen;].

Dynamical, Spectral, and Arithmetic Zeta Functions AMS Special Session on DynamicaL Spectral, and Arithmetic Zeta Functions JanuarySan Antonio, Texas Michel L. Lapidus Machiel van Frankenhuysen Editors American Mathematical Society Providence, Rhode Island.

The dynamical zeta functions of the geodesic flow of lo­ cally symmetric spaces of rank one are known also as the generalized Selberg zeta spectral.

The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were Cited by: J. Lagarias, "Number theory zeta functions and dynamical zeta functions", in Spectral Problems in Geometry and Arithmetic (T.

Branson, ed.), Contemporary Math. (AMS, ) [abstract:] "We describe analogies between number theory zeta functions, dynamical zeta functions,and statistical mechanics zeta functions, with emphasis on multi-variable zeta functions.

Our arguments are based on the study of the spectral properties of a transfer operator acting on suitable Banach spaces of anisotropic currents. Mass.: Benjamin/Cummings Publishing Co.

Inc. Advanced Book Program, Show bibtex. @book{AbrahamMarsden87, MRKEY={}, {Zeta functions and dynamical systems}, JOURNAL = {Nonlinearity}, Cited by: Dynamical, Spectral, and Arithmetic Zeta Functions About this Title. Michel L. Lapidus Dynamical Machiel van Frankenhuysen, Editors.

Publication: Contemporary Mathematics Publication Year Volume ISBNs: (print); (online). In mathematics, a zeta function is (usually) a function analogous to the original example: the Riemann zeta function = ∑ = ∞.Zeta functions include: Airy zeta function, related to the zeros of the Airy function; Arakawa–Kaneko zeta function; Arithmetic zeta function; Artin–Mazur zeta-function of a dynamical system; Barnes zeta function or double zeta function.

This second edition of Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, complex analysis, distribution theory, and mathematical spectral.

The significant studies and problems illuminated in this work may be used in a classroom Cited by: Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions.

The present book is concerned with these zeta functions from a cohomological point of view. The magnitude of the gradient of the 13 th eigenfunction of the Koch snowflake drum.

Research Interests. Mathematical Physics, Functional and Harmonic Analysis, Geometric Analysis, Partial Differential Equations (PDEs), Dynamical Systems, Spectral Geometry, Fractal Geometry; Connections with Number Theory, Arithmetic Geometry and Noncommutative Geometry.

Dynamical, spectral, and arithmetic zeta functions: AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions January, San Antonio, Texas / Michel L. Lapidus, Machiel.

This book is a collection of survey articles about spectral structures and the application of topological methods bridging different mathematical disciplines, from pure to applied. An overarching method is the use of zeta functions in the asymptotic counting of sublattices, group representations, etc.

Further examples connecting. From the Preface: These are the conference proceedings of the AMS Special Session on "Dynamical, Spectral and Artihmetic Zeta Functions" held at the Annual Meeting of the American Mathematical. This book is a collection of survey articles about spectral structures and the application of topological methods bridging different mathematical disciplines, from pure to applied.

The topics are based on work done in the Collaborative Research Centre (SFB) On the Nature of the “Explicit Formulas” in Analytic Number Theory — A Simple Example C. Deninger, W. Singhof, A note on dynamical trace formulas. In: M.L. Lapidus, M.

van Frankenhuysen (eds.), Dynamical Spectral and Arithmetic Zeta-Functions. In: AMS Contemp. Math. Deninger C. () On the Nature of the “Explicit Formulas Cited by: 8. [JA42] “Random Fractal Strings: Their Zeta Functions, Complex Dimensions and Spectral Asymptotics”, Transactions of the American Mathematical Society No.1, (), pp.(with B.

Details Dynamical, spectral, and arithmetic zeta functions EPUB

Hambly). When an ‘incollection’-type or ‘inproceedings’-type article is in a book which also appears in the collection, the book object just has the key “id”, whose value is the collection id of the book in quesiton.

Christopher Deninger (born 8 April ) is a German mathematician at the University of Münster. Deninger obtained his doctorate from the University of Cologne inunder the supervision of Curt he shared a Gottfried Wilhelm Leibniz Prize with Michael Rapoport, Peter Schneider and Thomas he was a plenary speaker at the International Congress of Mathematicians Doctoral advisor: Curt Meyer.

Periodic orbits and dynamical spectra function on 6A or 6C A, set fD ˙, and define the weighted dynamical zeta function of the pair.f;g/to be the formal power series g.z/D exp X1 nD1 zn n x2Fixfn nY−1 kD0 x/// where Fix.f/Dfx2 Xj f.x/D xg for any map f: Y.

Xwith Yˆ the case g 1, one recovers the Artin–Mazur unweighted dynamical zeta function (). The theory of Ihara zeta functions is extended to infinite graphs which are weighted and of finite total weight. In this case one gets meromorphic instead of rational functions and the classical determinant formulas of Bass and Ihara hold true with Fredholm by: 5.

Email your librarian or administrator to recommend adding this book to your organisation's collection. such as Bombieri's proof of the Riemann Hypothesis for function fields, along with an explanation of the connections with Nevanlinna theory and non-commutative geometry.

Dynamical, Spectral, and Arithmetic Zeta Functions (M. L Author: Machiel van Frankenhuijsen. Spectral. Welcome,you are looking at books for reading, the Spectral, you will able to read or download in Pdf or ePub books and notice some of author may have lock the live reading for some of ore it need a FREE signup process to obtain the book.

If it available for your country it will shown as book reader and user fully subscribe will benefit by having full access to all books. Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra.

Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a. We construct cross sections for the geodesic flow on the orbifolds $\Gamma $\$ \mathbb{H}$ which are tailor-made for the requirements of transfer operator approaches to Maass cusp forms and Selberg zeta functions.

Here, $\mathbb{H}$ denotes the hyperbolic plane and $\Gamma$ is a nonuniform geometrically finite Fuchsian group (not necessarily a lattice, not necessarily arithmetic) which Cited by: [Kotani and Sunada ] M.

Kotani and T. Sunada, “Zeta functions of finite graphs”, J. Math. Sci. Univ. Tokyo (), 7– [Lagarias ] J. Lagarias, “Number theory zeta functions and dynamical zeta functions”, pp. 45–86 in Spectral problems in geometry and arithmetic (Iowa City.

The Riemann-Siegel formula is an approximation formula for the Zeta function specifically on the critical line. Evaluation of the formula requires O(t 1/2) operations to evaluate a single value of Zeta( + t *i).This is in contrast to the faster Odlyzko - Schönhage method, which requires amortized O(t ε) operations per evaluation (where ε can be made arbitrarily small at the cost of a.

Spectral problems in geometry and arithmetic: Preface Thomas Branson In August,more than 50 participant.s came together for the NSF-CBMS conference "Spectral problems in geometry and arithmetic," with principal speaker Peter Sarnak.

Description Dynamical, spectral, and arithmetic zeta functions FB2

Among other. Abstract. For a geometrically finite hyperbolic surface X the Selberg zeta function Z X (s) was introduced in §The zeta function is associated with the length spectrum of X (or, equivalently, to traces of conjugacy classes of Γ).We will see in this chapter that it deserves to be thought of as a spectral invariant as well, by virtue of a beautiful correspondence between resonances of X Author: David Borthwick.

Graph theory meets number theory in this book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann or Dedekind zeta functions.

For example, there is a Riemann hypothesis (which may be false) and a prime number theorem for graphs. Pages in Proceedings of the Conference on Dynamical, Spectral and Arithmetic Zeta Functions, ed. M. van Frankenhuysen and M. L. Lapidus, Contemporary Mathematics Series, AMS, Providence, RI, [Ok] A note on the transcendental continued fractions (T.

.The Physics and Computational Exploration of Zeta and L-functions. Chris King Feb PDF (with full-size equations) Genotype Abstract: This article presents a spectrum of 4-D global portraits of a diversity of zeta and L-functions, using currently devised numerical methods and explores the implications of these functions in enriching the understanding of diverse areas in physics.

Appendices.- A Zeta Functions in Number Theory.- A.l The Dedekind Zeta Function.- A.3 Completion of L-Series, Functional Equation.- A.4 Epstein Zeta Functions.- A.5 Other Zeta Functions in Number Theory.- B Zeta Functions of Laplacians and Spectral Asymptotics.- B.l Weyl’s Asymptotic Formula.- B.2 Heat Asymptotic Expansion.-Author: Michel L.

Lapidus.