Number Theory Trace Formulas And Discrete Groups
DOWNLOAD eBooks
Download Number Theory Trace Formulas And Discrete Groups PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Number Theory Trace Formulas And Discrete Groups book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Number Theory Trace Formulas And Discrete Groups
DOWNLOAD eBooks
Author : Karl Egil Aubert
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Number Theory Trace Formulas And Discrete Groups written by Karl Egil Aubert and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Number Theory, Trace Formulas and Discrete Groups: Symposium in Honor of Atle Selberg Oslo, Norway, July 14-21, 1987 is a collection of papers presented at the 1987 Selberg Symposium, held at the University of Oslo. This symposium contains 30 lectures that cover the significant contribution of Atle Selberg in the field of mathematics. This book is organized into three parts encompassing 29 chapters. The first part presents a brief introduction to the history and developments of the zeta-function. The second part contains lectures on Selberg's considerable research studies on understanding the principles of several aspects of mathematics, including in modular forms, the Riemann zeta function, analytic number theory, sieve methods, discrete groups, and trace formula. The third part is devoted to Selberg's further research works on these topics, with particular emphasis on their practical applications. Some of these research studies, including the integral representations of Einstein series and L-functions; first eigenvalue for congruence groups; the zeta function of a Kleinian group; and the Waring's problem are discussed. This book will prove useful to mathematicians, researchers, and students.
Topics In Number Theory
DOWNLOAD eBooks
Author : Minking Eie
language : en
Publisher: World Scientific
Release Date : 2009
Topics In Number Theory written by Minking Eie and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This is a first-ever textbook written in English about the theory of modular forms and Jacobi forms of several variables. It contains the classical theory as well as a new theory on Jacobi forms over Cayley numbers developed by the author from 1990 to 2000. Applications to the classical Euler sums are of special interest to those who are eager to evaluate double Euler sums or more general multiple zeta values. The celebrated sum formula proved by Granville in 1997 is generalized to a more general form here.
Arithmetic Groups And Their Generalizations
DOWNLOAD eBooks
Author : Lizhen Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-20
Arithmetic Groups And Their Generalizations written by Lizhen Ji and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Mathematics categories.
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n,\mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA. Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come. (AMSIP/43.)
Representation Theory And Automorphic Forms
DOWNLOAD eBooks
Author : T. N. Bailey
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Representation Theory And Automorphic Forms written by T. N. Bailey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Automorphic forms categories.
The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR
Fourier Analysis On Finite Groups And Applications
DOWNLOAD eBooks
Author : Audrey Terras
language : en
Publisher: Cambridge University Press
Release Date : 1999-03-28
Fourier Analysis On Finite Groups And Applications written by Audrey Terras and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-28 with Mathematics categories.
It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Emerging Applications Of Number Theory
DOWNLOAD eBooks
Author : Dennis A. Hejhal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Emerging Applications Of Number Theory written by Dennis A. Hejhal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.
Advanced Analytic Number Theory L Functions
DOWNLOAD eBooks
Author : Carlos J. Moreno
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Advanced Analytic Number Theory L Functions written by Carlos J. Moreno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Algebraic number theory categories.
Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.
The Heat Kernel And Theta Inversion On Sl2 C
DOWNLOAD eBooks
Author : Jay Jorgenson
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-20
The Heat Kernel And Theta Inversion On Sl2 C written by Jay Jorgenson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-20 with Mathematics categories.
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the author's previous work, the inversion formula then leads to zeta functions through the Gauss transform./
Harmonic Analysis On Symmetric Spaces Higher Rank Spaces Positive Definite Matrix Space And Generalizations
DOWNLOAD eBooks
Author : Audrey Terras
language : en
Publisher: Springer
Release Date : 2016-04-26
Harmonic Analysis On Symmetric Spaces Higher Rank Spaces Positive Definite Matrix Space And Generalizations written by Audrey Terras and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-26 with Mathematics categories.
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.
Dynamics Geometry Number Theory
DOWNLOAD eBooks
Author : David Fisher
language : en
Publisher: University of Chicago Press
Release Date : 2022-02-07
Dynamics Geometry Number Theory written by David Fisher and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-07 with Mathematics categories.
"Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--