Download or read book The Meromorphic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Subgroups written by Shek-Tung Wong and published by American Mathematical Soc.. This book was released on 1990 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: We carry out, in the context of an algebraic group and an arithmetic subgroup, an idea of Selberg for continuing Eisenstein series. It makes use of the theory of integral operators. The meromorphic continuation and functional equation of an Eisenstein series constructed with a cusp form on the Levi component of a rank one cuspidal subgroup are established.
Download or read book On the Functional Equations Satisfied by Eisenstein Series written by Robert P. Langlands and published by Lecture Notes in Mathematics. This book was released on 1976-10-20 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction.- Statement of assumptions. Some properties of discrete groups satisfying the assumptions.- Definition of a cusp form (after Gelfand). Basic properties of cusp forms.- Definition of Eisenstein series. Investigation of the constant term in the Fourier expansion of an Eisenstein series. A variant of a formula of Selberg.- Some lemmas used in Sections 6 and 7.- Proof of the function equations for the Eisenstein series associated to cusp forms.- Proof of the functional equations for all Eisenstein series. Statement of theorem.- References.- Appendices
Download or read book Imbeddings of Three Manifold Groups written by Francisco González-Acuña and published by American Mathematical Soc.. This book was released on 1992 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with the two broad questions of how 3-manifold groups imbed in one another and how such imbeddings relate to any corresponding [lowercase Greek]Pi1-injective maps. In particular, we are interested in 1) determining which 3-manifold groups are no cohopfian, that is, which 3-manifold groups imbed properly in themselves, 2) determining the knot subgroups of a knot group, and 3) determining when surgery on a knot [italic]K yields a lens (or "lens-like") space and the relationship of such a surgery to the knot-subgroup structure of [lowercase Greek]Pi1([italic]S3 - [italic]K). Our work requires the formulation of a deformation theorem for [lowercase Greek]Pi1-injective maps between certain kinds of Haken manifolds and the development of some algebraic tools.
Download or read book Harmonic Analysis on Symmetric Spaces Higher Rank Spaces Positive Definite Matrix Space and Generalizations written by Audrey Terras and published by Springer. This book was released on 2016-04-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for beginning graduate students in mathematics or researchers in physics or engineering. As with the introductory book entitled "Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincaré Upper Half Plane, the style is informal with an emphasis on motivation, concrete examples, history, and applications. The symmetric spaces considered here are quotients X=G/K, where G is a non-compact real Lie group, such as the general linear group GL(n,P) of all n x n non-singular real matrices, and K=O(n), the maximal compact subgroup of orthogonal matrices. Other examples are Siegel's upper half "plane" and the quaternionic upper half "plane". In the case of the general linear group, one can identify X with the space Pn of n x n positive definite symmetric matrices. Many corrections and updates have been incorporated in this new edition. Updates include discussions of random matrix theory and quantum chaos, as well as recent research on modular forms and their corresponding L-functions in higher rank. Many applications have been added, such as the solution of the heat equation on Pn, the central limit theorem of Donald St. P. Richards for Pn, results on densest lattice packing of spheres in Euclidean space, and GL(n)-analogs of the Weyl law for eigenvalues of the Laplacian in plane domains. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, fundamental domains in X for discrete groups Γ (such as the modular group GL(n,Z) of n x n matrices with integer entries and determinant ±1), connections with the problem of finding densest lattice packings of spheres in Euclidean space, automorphic forms, Hecke operators, L-functions, and the Selberg trace formula and its applications in spectral theory as well as number theory.
Download or read book A Generalization of Riemann Mappings and Geometric Structures on a Space of Domains in C n written by Stephen Semmes and published by American Mathematical Soc.. This book was released on 1992 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Similar in philosophy to the study of moduli spaces in algebraic geometry, the central theme of this book is that spaces of (pseudoconvex) domains should admit geometrical structures that reflect the complex geometry of the underlying domains in a natural way. With its unusual geometric perspective of some topics in several complex variables, this book appeals to those who view much of mathematics in broadly geometrical terms.
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1989 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to the Langlands Program written by D. Bump and published by Springer Science & Business Media. This book was released on 2003-05-20 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
Download or read book Spectral Decomposition and Eisenstein Series written by Colette Moeglin and published by Cambridge University Press. This book was released on 1995-11-02 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.
Download or read book Lectures on Automorphic L functions written by James W. Cogdell and published by American Mathematical Soc.. This book was released on with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: James W. Cogdell, Lectures on $L$-functions, converse theorems, and functoriality for $GL_n$: Preface Modular forms and their $L$-functions Automorphic forms Automorphic representations Fourier expansions and multiplicity one theorems Eulerian integral representations Local $L$-functions: The non-Archimedean case The unramified calculation Local $L$-functions: The Archimedean case Global $L$-functions Converse theorems Functoriality Functoriality for the classical groups Functoriality for the classical groups, II Henry H. Kim, Automorphic $L$-functions: Introduction Chevalley groups and their properties Cuspidal representations $L$-groups and automorphic $L$-functions Induced representations Eisenstein series and constant terms $L$-functions in the constant terms Meromorphic continuation of $L$-functions Generic representations and their Whittaker models Local coefficients and non-constant terms Local Langlands correspondence Local $L$-functions and functional equations Normalization of intertwining operators Holomorphy and bounded in vertical strips Langlands functoriality conjecture Converse theorem of Cogdell and Piatetski-Shapiro Functoriality of the symmetric cube Functoriality of the symmetric fourth Bibliography M. Ram Murty, Applications of symmetric power $L$-functions: Preface The Sato-Tate conjecture Maass wave forms The Rankin-Selberg method Oscillations of Fourier coefficients of cusp forms Poincare series Kloosterman sums and Selberg's conjecture Refined estimates for Fourier coefficients of cusp forms Twisting and averaging of $L$-series The Kim-Sarnak theorem Introduction to Artin $L$-functions Zeros and poles of Artin $L$-functions The Langlands-Tunnell theorem Bibliography
Download or read book Mathematical Reviews written by and published by . This book was released on 2000 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Duality for Actions and Coactions of Measured Groupoids on von Neumann Algebras written by Takehiko Yamanouchi and published by American Mathematical Soc.. This book was released on 1993 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through classification of compact abelian group actions on semifinite injective factors, Jones and Takesaki introduced a notion of an action of a measured groupoid on a von Neumann algebra, which was proven to be an important tool for such an analysis. In this paper, elaborating their definition, the author introduces a new concept of a measured groupoid action that may fit more perfectly in the groupoid setting. The author also considers a notion of a coaction of a measured groupoid by showing the existence of a canonical "coproduct" on every groupoid von Neumann algebra.
Download or read book Semistability of Amalgamated Products and HNN Extensions written by Michael L. Mihalik and published by American Mathematical Soc.. This book was released on 1992 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the authors show that amalgamated products and HNN-extensions of finitely presented semistable at infinity groups are also semistable at infinity. A major step toward determining whether all finitely presented groups are semistable at infinity, this result easily generalizes to finite graphs of groups. The theory of group actions on trees and techniques derived from the proof of Dunwoody's accessibility theorem are key ingredients in this work.
Download or read book Manuscripta Mathematica written by and published by . This book was released on 1992 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Eisenstein Series and Automorphic L Functions written by Freydoon Shahidi and published by American Mathematical Soc.. This book was released on 2010 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.
Download or read book G Categories written by Robert Gordon and published by American Mathematical Soc.. This book was released on 1993 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: A [italic]G-category is a category on which a group [italic]G acts. This work studies the 2-category [italic]G-cat of [italic]G-categories, [italic]G-functors (functors which commute with the action of [italic]G) and [italic]G-natural transformations (natural transformations which commute with the [italic]G-action). There is a particular emphasis on the relationship between a [italic]G-category and its stable subcategory, the largest sub-[italic]G-category on which [italic]G operates trivially. Also contained here are some very general applications of the theory to various additive [italic]G-categories and to [italic]G-topoi.
Download or read book Eigenvalues of the Laplacian for Hecke Triangle Groups written by Dennis A. Hejhal and published by American Mathematical Soc.. This book was released on 1992 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On the Existence of Feller Semigroups with Boundary Conditions written by Kazuaki Taira and published by American Mathematical Soc.. This book was released on 1992 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with Ventcel' (Wentzell) boundary conditions. This paper considers the non-transversal case and solves from the viewpoint of functional analysis the problem of construction of Feller semigroups for elliptic Waldenfels operators. Intuitively, our result may be stated as follows: One can construct a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it "dies" at which time it reaches the set where the absorption phenomenon occurs.
