# The Selberg Arthur Trace Formula

Produk Detail:
• Author : Salahoddin Shokranian
• Publisher : Springer
• Pages : 99 pages
• ISBN : 3540466592
• Rating : /5 from reviews

## The Selberg Arthur Trace Formula

• Author : Salahoddin Shokranian
• Publisher : Springer
• Release : 14 November 2006

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

## Lectures on the Arthur Selberg Trace Formula

• Author : Stephen S. Gelbart
• Publisher : American Mathematical Soc.
• Release : 29 November 1996

This work offers for the first time a simultaneous treatment of a general group with the case of GL(2). It also treats the trace formula with the example of Jacquet's relative formula.

## The Selberg Arthur Trace Formula

• Author : Salahoddin Shokranian
• Publisher : Springer
• Release : 12 February 1992

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

• Author : Mechthild Stoer
• Publisher : Springer
• Release : 14 December 1992

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

• Author : Andrew Knightly,Charles Li
• Publisher : American Mathematical Soc.
• Release : 29 November 2021

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

• Author : Werner Müller,Sug Woo Shin,Nicolas Templier
• Publisher : Springer
• Release : 20 September 2016

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

• Author : Clay Mathematics Institute. Summer School,Clay Mathematics Institute
• Publisher : American Mathematical Soc.
• Release : 29 November 2021

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

• Author : Yuval Z. Flicker
• Publisher : Birkhäuser
• Release : 14 September 2016

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

## On the Stabilization of the Trace Formula

• Author : Laurent Clozel,Michael Harris,Jean-Pierre Labesse,Bao-Châu Ngô
• Publisher : International Pressof Boston Incorporated
• Release : 29 November 2021

## Mathematics without Apologies

• Author : Michael Harris
• Publisher : Princeton University Press
• Release : 30 May 2017

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

• Author : Werner Hoffmann,Satoshi Wakatsuki
• Publisher : American Mathematical Soc.
• Release : 03 October 2018

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

• Author : Andrew Knightly,C. Li
• Publisher : American Mathematical Soc.
• Release : 28 June 2013

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

• Author : Werner Müller,Sug Woo Shin,Nicolas Templier
• Publisher : Springer
• Release : 11 October 2018

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

• Author : Nicolas Bergeron
• Publisher : Springer
• Release : 19 February 2016

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