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Author: Laurent Clozel
Publisher:
ISBN: 9781571463555
Category :
Languages : en
Pages : 542
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Book Description
This is the first volume of a projected series of two or three collections of mainly expository articles on the arithmetic theory of automorphic forms. The books are intended primarily for two groups of readers. The first group is interested in the structure of automorphic forms on reductive groups over number fields, and specifically in qualitative information about the multiplicities of automorphic representations. The second group is interested in the problem of classifying l-adic representations of Galois groups of number fields. Langlands' conjectures elaborate on the notion that these two problems overlap to a considerable degree. The goal of this series of books is to gather into one place much of the evidence that this is the case, and to present it clearly and succinctly enough so that both groups of readers are not only convinced by the evidence but can pass with minimal effort between the two points of view. More than a decade's worth of progress toward the stabilization of the Arthur-Selberg trace formula, culminating in Ngô Bau Châu's recent proof of the Fundamental Lemma, has made this series timely.
Author: Laurent Clozel
Publisher:
ISBN: 9781571463555
Category :
Languages : en
Pages : 542
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Book Description
This is the first volume of a projected series of two or three collections of mainly expository articles on the arithmetic theory of automorphic forms. The books are intended primarily for two groups of readers. The first group is interested in the structure of automorphic forms on reductive groups over number fields, and specifically in qualitative information about the multiplicities of automorphic representations. The second group is interested in the problem of classifying l-adic representations of Galois groups of number fields. Langlands' conjectures elaborate on the notion that these two problems overlap to a considerable degree. The goal of this series of books is to gather into one place much of the evidence that this is the case, and to present it clearly and succinctly enough so that both groups of readers are not only convinced by the evidence but can pass with minimal effort between the two points of view. More than a decade's worth of progress toward the stabilization of the Arthur-Selberg trace formula, culminating in Ngô Bau Châu's recent proof of the Fundamental Lemma, has made this series timely.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Laurent Clozel
Publisher: International Pressof Boston Incorporated
ISBN: 9781571462275
Category : Mathematics
Languages : en
Pages : 527
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Book Description
Author: Clay Mathematics Institute. Summer School
Publisher: American Mathematical Soc.
ISBN: 9780821838440
Category : Mathematics
Languages : en
Pages : 708
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Book Description
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.
Author: Werner Müller
Publisher: Springer
ISBN: 3319948334
Category : Mathematics
Languages : en
Pages : 453
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Book Description
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 of Langlands and Arthur packets, interactions with geometric representation theory, and conjectures on the global automorphic spectrum. Suitable for both graduate students and researchers, this volume presents the latest research in the field. Readers of the first volume Families of Automorphic Forms and the Trace Formula will find this a natural continuation of the study of the trace formula.
Author: Werner Müller
Publisher: Springer
ISBN: 3319414240
Category : Mathematics
Languages : en
Pages : 581
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Book Description
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 the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
Author: Akshay Venkatesh
Publisher:
ISBN:
Category :
Languages : en
Pages : 336
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Book Description
Author: Werner Hoffmann
Publisher: American Mathematical Soc.
ISBN: 1470431025
Category :
Languages : en
Pages : 88
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Book Description
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.
Author: Salahoddin Shokranian
Publisher: Springer
ISBN: 3540466592
Category : Mathematics
Languages : en
Pages : 104
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Book Description
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
Author: Werner Müller
Publisher: Springer Nature
ISBN: 3030685063
Category : Mathematics
Languages : en
Pages : 438
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Book Description
A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.