The Selberg Arthur Trace Formula

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  • Author : Salahoddin Shokranian
  • Publisher : Springer
  • Pages : 99 pages
  • ISBN : 3540466592
  • Rating : /5 from reviews
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Download or Read online The Selberg Arthur Trace Formula full in PDF, ePub and kindle. this book written by Salahoddin Shokranian and published by Springer which was released on 14 November 2006 with total page 99 pages. We cannot guarantee that The Selberg Arthur Trace Formula book is available in the library, click Get Book button and read full online book in your kindle, tablet, IPAD, PC or mobile whenever and wherever You Like. This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks

The Selberg Arthur Trace Formula

The Selberg Arthur Trace Formula
  • Author : Salahoddin Shokranian
  • Publisher : Springer
  • Release : 14 November 2006
GET THIS BOOK The Selberg Arthur Trace Formula

This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular

The Selberg Arthur Trace Formula

The Selberg Arthur Trace Formula
  • Author : Salahoddin Shokranian
  • Publisher : Springer
  • Release : 12 February 1992
GET THIS BOOK The Selberg Arthur Trace Formula

This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular

Design of Survivable Networks

Design of Survivable Networks
  • Author : Mechthild Stoer
  • Publisher : Springer
  • Release : 14 December 1992
GET THIS BOOK Design of Survivable Networks

The problem of designing a cost-efficient network that survives the failure of one or more nodes or edges of the network is critical to modern telecommunications engineering. The method developed in this book is designed to solve such problems to optimality. In particular, a cutting plane approach is described, based on polyhedral combinatorics, that is ableto solve real-world problems of this type in short computation time. These results are of interest for practitioners in the area of communication network design.

Traces of Hecke Operators

Traces of Hecke Operators
  • Author : Andrew Knightly,Charles Li
  • Publisher : American Mathematical Soc.
  • Release : 29 November 2021
GET THIS BOOK Traces of Hecke Operators

The Fourier coefficients of modular forms are of widespread interest as an important source of arithmetic information. In many cases, these coefficients can be recovered from explicit knowledge of the traces of Hecke operators. The original trace formula for Hecke operators was given by Selberg in 1956. Many improvements were made in subsequent years, notably by Eichler and Hijikata. This book provides a comprehensive modern treatment of the Eichler-Selberg/Hijikata trace formula for the traces of Hecke operators on spaces of

Families of Automorphic Forms and the Trace Formula

Families of Automorphic Forms and the Trace Formula
  • Author : Werner Müller,Sug Woo Shin,Nicolas Templier
  • Publisher : Springer
  • Release : 20 September 2016
GET THIS BOOK Families of Automorphic Forms and the Trace Formula

Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in

Harmonic Analysis the Trace Formula and Shimura Varieties

Harmonic Analysis  the Trace Formula  and Shimura Varieties
  • Author : Clay Mathematics Institute. Summer School,Clay Mathematics Institute
  • Publisher : American Mathematical Soc.
  • Release : 29 November 2021
GET THIS BOOK Harmonic Analysis the Trace Formula and Shimura Varieties

Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.

Arthur s Invariant Trace Formula and Comparison of Inner Forms

Arthur s Invariant Trace Formula and Comparison of Inner Forms
  • Author : Yuval Z. Flicker
  • Publisher : Birkhäuser
  • Release : 14 September 2016
GET THIS BOOK Arthur s Invariant Trace Formula and Comparison of Inner Forms

This monograph provides an accessible and comprehensive introduction to James Arthur’s invariant trace formula, a crucial tool in the theory of automorphic representations. It synthesizes two decades of Arthur’s research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details. The book begins with a brief overview of Arthur’s work and a proof of the correspondence between GL(n) and its inner

Mathematics without Apologies

Mathematics without Apologies
  • Author : Michael Harris
  • Publisher : Princeton University Press
  • Release : 30 May 2017
GET THIS BOOK Mathematics without Apologies

An insightful reflection on the mathematical soul What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and

On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2

On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2
  • Author : Werner Hoffmann,Satoshi Wakatsuki
  • Publisher : American Mathematical Soc.
  • Release : 03 October 2018
GET THIS BOOK On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2

The authors study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank over any algebraic number field. In particular, they express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke -functions, and the Shintani zeta function for the space of binary quadratic forms.

Kuznetsov s Trace Formula and the Hecke Eigenvalues of Maass Forms

Kuznetsov s Trace Formula and the Hecke Eigenvalues of Maass Forms
  • Author : Andrew Knightly,C. Li
  • Publisher : American Mathematical Soc.
  • Release : 28 June 2013
GET THIS BOOK Kuznetsov s Trace Formula and the Hecke Eigenvalues of Maass Forms

The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when

Geometric Aspects of the Trace Formula

Geometric Aspects of the Trace Formula
  • Author : Werner Müller,Sug Woo Shin,Nicolas Templier
  • Publisher : Springer
  • Release : 11 October 2018
GET THIS BOOK Geometric Aspects of the Trace Formula

The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the field. The articles discuss topics such as the classification problem of representations of reductive groups, the structure

The Spectrum of Hyperbolic Surfaces

The Spectrum of Hyperbolic Surfaces
  • Author : Nicolas Bergeron
  • Publisher : Springer
  • Release : 19 February 2016
GET THIS BOOK The Spectrum of Hyperbolic Surfaces

This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace