Selberg Trace Formulae And Equidistribution Theorems For Closed Geodesics And Laplace

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Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace

Steven Zelditch
Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace Book PDF

Author : Steven Zelditch
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 51,7 Mb
Release : 1992
Category : Curves on surfaces
ISBN : 9780821825266

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Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace by Steven Zelditch Pdf

This work is concerned with a pair of dual asymptotics problems on a finite-area hyperbolic surface. The first problem is to determine the distribution of closed geodesics in the unit tangent bundle. The second problem is to determine the distribution of eigenfunctions (in microlocal sense) in the unit tangent bundle.

Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace Eigenfunctions

Steven Zelditch
Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace Eigenfunctions Book PDF

Author : Steven Zelditch
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 42,6 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821861883

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Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace Eigenfunctions by Steven Zelditch Pdf

This work is concerned with a pair of dual asymptotics problems on a finite-area hyperbolic surface. The first problem is to determine the distribution of closed geodesics in the unit tangent bundle. The second problem is to determine the distribution of eigenfunctions (in microlocal sense) in the unit tangent bundle.

Cohomological Theory of Dynamical Zeta Functions

Andreas Juhl
Cohomological Theory of Dynamical Zeta Functions Book PDF

Author : Andreas Juhl
Publisher : Birkhäuser
Page : 712 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883405

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Cohomological Theory of Dynamical Zeta Functions by Andreas Juhl Pdf

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. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.

Quantum Chaos and Mesoscopic Systems

N.E. Hurt
Quantum Chaos and Mesoscopic Systems Book PDF

Author : N.E. Hurt
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 51,9 Mb
Release : 1997-02-28
Category : Mathematics
ISBN : 0792344596

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Quantum Chaos and Mesoscopic Systems by N.E. Hurt Pdf

4. 2 Variance of Quantum Matrix Elements. 125 4. 3 Berry's Trick and the Hyperbolic Case 126 4. 4 Nonhyperbolic Case . . . . . . . 128 4. 5 Random Matrix Theory . . . . . 128 4. 6 Baker's Map and Other Systems 129 4. 7 Appendix: Baker's Map . . . . . 129 5 Error Terms 133 5. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 133 5. 2 The Riemann Zeta Function in Periodic Orbit Theory 135 5. 3 Form Factor for Primes . . . . . . . . . . . . . . . . . 137 5. 4 Error Terms in Periodic Orbit Theory: Co-compact Case. 138 5. 5 Binary Quadratic Forms as a Model . . . . . . . . . . . . 139 6 Co-Finite Model for Quantum Chaology 141 6. 1 Introduction. . . . . . . . 141 6. 2 Co-finite Models . . . . . 141 6. 3 Geodesic Triangle Spaces 144 6. 4 L-Functions. . . . . . . . 145 6. 5 Zelditch's Prime Geodesic Theorem. 146 6. 6 Zelditch's Pseudo Differential Operators 147 6. 7 Weyl's Law Generalized 148 6. 8 Equidistribution Theory . . . . . . . . . 150 7 Landau Levels and L-Functions 153 7. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 153 7. 2 Landau Model: Mechanics on the Plane and Sphere. 153 7. 3 Landau Model: Mechanics on the Half-Plane 155 7. 4 Selberg's Spectral Theorem . . . . . . . . . . . 157 7. 5 Pseudo Billiards . . . . . . . . . . . . . . . . . 158 7. 6 Landau Levels on a Compact Riemann Surface 159 7. 7 Automorphic Forms . . . . . 160 7. 8 Maass-Selberg Trace Formula 162 7. 9 Degeneracy by Selberg. . . . 163 7. 10 Hecke Operators . . . . . . . 163 7. 11 Selberg Trace Formula for Hecke Operators 167 7. 12 Eigenvalue Statistics on X . . . . 169 7. 13 Mesoscopic Devices. . . . . . . . 170 7. 14 Hall Conductance on Leaky Tori 170 7.

The Kinematic Formula in Riemannian Homogeneous Spaces

Ralph Howard
The Kinematic Formula in Riemannian Homogeneous Spaces Book PDF

Author : Ralph Howard
Publisher : American Mathematical Soc.
Page : 69 pages
File Size : 43,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825693

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The Kinematic Formula in Riemannian Homogeneous Spaces by Ralph Howard Pdf

This book shows that much of classical integral geometry can be derived from the coarea formula by some elementary techniques. Howard generalizes much of classical integral geometry from spaces of constant sectional curvature to arbitrary Riemannian homogeneous spaces. To do so, he provides a general definition of an ``integral invariant'' of a submanifold of the space that is sufficiently general enough to cover most cases that arise in integral geometry. Working in this generality makes it clear that the type of integral geometric formulas that hold in a space does not depend on the full group of isometries, but only on the isotropy subgroup. As a special case, integral geometric formulas that hold in Euclidean space also hold in all the simply connected spaces of constant curvature. Detailed proofs of the results and many examples are included. Requiring background of a one-term course in Riemannian geometry, this book may be used as a textbook in graduate courses on differential and integral geometry.

Eigenvalues of the Laplacian for Hecke Triangle Groups

Dennis A. Hejhal
Eigenvalues of the Laplacian for Hecke Triangle Groups Book PDF

Author : Dennis A. Hejhal
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 44,7 Mb
Release : 1992
Category : Automorphic functions
ISBN : 9780821825297

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Eigenvalues of the Laplacian for Hecke Triangle Groups by Dennis A. Hejhal Pdf

Paper I is concerned with computational aspects of the Selberg trace formalism, considering the usual type of eigenfunction and including an analysis of pseudo cusp forms and their residual effects. Paper II examines the modular group PSL (2, [bold]Z), as such groups have both a discrete and continuous spectrum. This paper only examines the discrete side of the spectrum.

Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds

Takashi Shioya
Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2 dimensional Riemannian Manifolds Book PDF

Author : Takashi Shioya
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 40,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825785

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Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds by Takashi Shioya Pdf

This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.

Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory

David Soudry
Rankin Selberg Convolutions for SO 2 1GL n Local Theory Book PDF

Author : David Soudry
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 53,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825686

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Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory by David Soudry Pdf

This work studies the local theory for certain Rankin-Selberg convolutions for the standard $L$-function of degree $21n$ of generic representations of $\textnormal{SO}_{2\ell +1}(F)\times \textnormal{GL}_n(F)$ over a local field $F$. The local integrals converge in a half-plane and continue meromorphically to the whole plane. One main result is the existence of local gamma and $L$-factors. The gamma factor is obtained as a proportionality factor of a functional equation satisfied by the local integrals. In addition, Soudry establishes the multiplicativity of the gamma factor ($1

Brownian Motion on Nested Fractals

Tom Lindstrøm
Brownian Motion on Nested Fractals Book PDF

Author : Tom Lindstrøm
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 51,6 Mb
Release : 1990-01
Category : Mathematics
ISBN : 9780821824849

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Brownian Motion on Nested Fractals by Tom Lindstrøm Pdf

Lindstrom (U. of Oslo) constructs Brownian motion on a reasonably general class of self-similar fractals. He deals with diffusions, self-similar fractals, fractal Laplacians, asymptotic distribution of eigenvalues, nonstandard analysis. Annotation copyright Book News, Inc. Portland, Or.

Deformation Quantization for Actions of $R^d$

Marc Aristide Rieffel
Deformation Quantization for Actions of R d Book PDF

Author : Marc Aristide Rieffel
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 50,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825754

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Deformation Quantization for Actions of $R^d$ by Marc Aristide Rieffel Pdf

This work describes a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of $R^d$ on that manifold. These deformation quantizations are strict, in the sense that the deformed product of any two functions is again a function and that there are corresponding involutions and operator norms. Many of the techniques involved are adapted from the theory of pseudo-differential operators. The construction is shown to have many favorable properties. A number of specific examples are described, ranging from basic ones such as quantum disks, quantum tori, and quantum spheres, to aspects of quantum groups.

Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations

Jaume Llibre,Ana Nunes
Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations Book PDF

Author : Jaume Llibre,Ana Nunes
Publisher : American Mathematical Soc.
Page : 191 pages
File Size : 52,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825815

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Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations by Jaume Llibre,Ana Nunes Pdf

This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the critical leaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonian perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of 'almost all' the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.

The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks

George E. Andrews
The Continued Fractions Found in the Unorganized Portions of Ramanujan s Notebooks Book PDF

Author : George E. Andrews
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 46,5 Mb
Release : 1992
Category : Continued fractions
ISBN : 9780821825389

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The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks by George E. Andrews Pdf

Among his thirty-three published papers, Ramanujan had only one continued fraction, the Rogers-Ramanujan continued fraction. However, his notebooks contain over 100 results on continued fractions. At the end of his second notebook are 100 pages of unorganized material, and the third notebook comprises thirty-three pages of disorganized results. In these 133 pages of material are approximately sixty theorems on continued fractions, most of them new results. In this monograph, the authors discuss and prove each of these theorems. Aimed at those interested in Ramanujan and his work, this monograph will be of special interest to those who work in continued fractions q -series, special function, theta-functions, and combinatorics. The work is likely to be of interest to those in number theory as well. The only required background is some knowledge of continued fractions and a course in complex analysis.

Constant Mean Curvature Immersions of Enneper Type

Henry C. Wente
Constant Mean Curvature Immersions of Enneper Type Book PDF

Author : Henry C. Wente
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 49,6 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825365

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Constant Mean Curvature Immersions of Enneper Type by Henry C. Wente Pdf

This memoir is devoted to the case of constant mean curvature surfaces immersed in [bold]R3. We reduce this geometrical problem to finding certain integrable solutions to the Gauss equation. Many new and interesting examples are presented, including immersed cylinders in [bold]R3 with embedded Delaunay ends and [italic]n-lobes in the middle, and one-parameter families of immersed constant mean curvature tori in [bold]R3. We examine minimal surfaces in hyperbolic three-space, which is in some ways the most complicated case.

An Index of a Graph with Applications to Knot Theory

Kunio Murasugi,Józef Przytycki
An Index of a Graph with Applications to Knot Theory Book PDF

Author : Kunio Murasugi,Józef Przytycki
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 55,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825709

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An Index of a Graph with Applications to Knot Theory by Kunio Murasugi,Józef Przytycki Pdf

This book presents a remarkable application of graph theory to knot theory. In knot theory, there are a number of easily defined geometric invariants that are extremely difficult to compute; the braid index of a knot or link is one example. The authors evaluate the braid index for many knots and links using the generalized Jones polynomial and the index of a graph, a new invariant introduced here. This invariant, which is determined algorithmically, is likely to be of particular interest to computer scientists.

On the Existence of Feller Semigroups with Boundary Conditions

Kazuaki Taira
On the Existence of Feller Semigroups with Boundary Conditions Book PDF

Author : Kazuaki Taira
Publisher : American Mathematical Soc.
Page : 65 pages
File Size : 49,5 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825358

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On the Existence of Feller Semigroups with Boundary Conditions by Kazuaki Taira Pdf

This monograph provides a careful and accessible exposition of functional analytic methods in stochastic analysis. The author focuses on the relationship among three subjects in analysis: Markov processes, Feller semigroups, and elliptic boundary value problems. The approach here is distinguished by the author's extensive use of the theory of partial differential equations. Filling a mathematical gap between textbooks on Markov processes and recent developments in analysis, this work describes a powerful method capable of extensive further development. The book would be suitable as a textbook in a one-year, advanced graduate course on functional analysis and partial differential equations, with emphasis on their strong interrelations with probability theory.