Relative Trace Formulas
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Relative Trace Formulas
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Author : Werner Müller
language : en
Publisher: Springer Nature
Release Date : 2021-05-18
Relative Trace Formulas written by Werner Müller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-18 with Mathematics categories.
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.
On The Spectral Expansion Of A Relative Trace Formula
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Author : K. F. Lai
language : en
Publisher:
Release Date : 1992
On The Spectral Expansion Of A Relative Trace Formula written by K. F. Lai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Spectral theory (Mathematics) categories.
A Local Relative Trace Formula For The Ginzburg Rallis Model The Geometric Side
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Author : Chen Wan
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-02
A Local Relative Trace Formula For The Ginzburg Rallis Model The Geometric Side written by Chen Wan 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 2019-12-02 with Education categories.
Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.
Lectures On The Arthur Selberg Trace Formula
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Author : Stephen S. Gelbart
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lectures On The Arthur Selberg Trace Formula written by Stephen S. Gelbart 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 1996 with Selberg trace formula categories.
The Arthur-Selberg trace formula is an equality between two kinds of traces: the geometric terms given by the conjugacy classes of a group and the spectral terms given by the induced representations. In general, these terms require a truncation in order to converge, which leads to an equality of truncated kernels. The formulas are difficult in general and even the case of $GL$(2) is nontrivial. The book gives proof of Arthur's trace formula of the 1970s and 1980s, with special attention given to $GL$(2). The problem is that when the truncated terms converge, they are also shown to be polynomial in the truncation variable and expressed as ``weighted'' orbital and ``weighted'' characters. In some important cases the trace formula takes on a simple form over $G$. The author gives some examples of this, and also some examples of Jacquet's relative trace formula. 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. Features: Discusses why the terms of the geometric and spectral type must be truncated, and why the resulting truncations are polynomials in the truncation of value $T$. Brings into play the significant tool of ($G, M$) families and how the theory of Paley-Weiner is applied. Explains why the truncation formula reduces to a simple formula involving only the elliptic terms on the geometric sides with the representations appearing cuspidally on the spectral side (applies to Tamagawa numbers). Outlines Jacquet's trace formula and shows how it works for $GL$(2).
Kuznetsov S Trace Formula And The Hecke Eigenvalues Of Maass Forms
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Author : Andrew Knightly
language : en
Publisher:
Release Date : 2013
Kuznetsov S Trace Formula And The Hecke Eigenvalues Of Maass Forms written by Andrew Knightly and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Hecke operators categories.
Automorphic Representations L Functions And Applications
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Author : Stephen Rallis
language : en
Publisher: Walter de Gruyter
Release Date : 2005
Automorphic Representations L Functions And Applications written by Stephen Rallis and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27-30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin-Selberg L-functions (Bump, Ginzburg-Jiang-Rallis, Lapid-Rallis) the relative trace formula (Jacquet, Mao-Rallis) automorphic representations (Gan-Gurevich, Ginzburg-Rallis-Soudry) representation theory of p-adic groups (Baruch, Kudla-Rallis, Moeglin, Cogdell-Piatetski-Shapiro-Shahidi) p-adic methods (Harris-Li-Skinner, Vigneras), and arithmetic applications (Chinta-Friedberg-Hoffstein). The survey articles by Bump, on the Rankin-Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.
Relative Aspects In Representation Theory Langlands Functoriality And Automorphic Forms
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Author : Volker Heiermann
language : en
Publisher: Springer
Release Date : 2018-10-01
Relative Aspects In Representation Theory Langlands Functoriality And Automorphic Forms written by Volker Heiermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-01 with Mathematics categories.
This volume presents a panorama of the diverse activities organized by V. Heiermann and D. Prasad in Marseille at the CIRM for the Chaire Morlet event during the first semester of 2016. It assembles together expository articles on topics which previously could only be found in research papers. Starting with a very detailed article by P. Baumann and S. Riche on the geometric Satake correspondence, the book continues with three introductory articles on distinguished representations due to P. Broussous, F. Murnaghan, and O. Offen; an expository article of I. Badulescu on the Jacquet–Langlands correspondence; a paper of J. Arthur on functoriality and the trace formula in the context of "Beyond Endoscopy", taken from the Simons Proceedings; an article of W-W. Li attempting to generalize Godement–Jacquet theory; and a research paper of C. Moeglin and D. Renard, applying the trace formula to the local Langlands classification for classical groups. The book should be of interest to students as well as professional researchers working in the broad area of number theory and representation theory.
A Local Trace Formula
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Author : James Arthur
language : en
Publisher:
Release Date : 1989
A Local Trace Formula written by James Arthur and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Automorphic forms categories.
Local Analysis Of Selberg S Trace Formula
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Author : A. Good
language : en
Publisher:
Release Date : 2014-01-15
Local Analysis Of Selberg S Trace Formula written by A. Good and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Number Theory Trace Formulas And Discrete Groups
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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.