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Relative Trace Formulas

2021-05-18 Mathematics
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Release : 2021-05-18
Genre : Mathematics
Kind : eBook
Book Rating : 063/5 ( reviews)

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Book Synopsis Relative Trace Formulas by : Werner Müller

Download or read book Relative Trace Formulas written by Werner Müller. This book was released on 2021-05-18. Available in PDF, EPUB and Kindle. Book excerpt: 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 Local Relative Trace Formula

2009 Trace formulas
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Release : 2009
Genre : Trace formulas
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis On the Local Relative Trace Formula by : Jonathan Sparling

Download or read book On the Local Relative Trace Formula written by Jonathan Sparling. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt:

Families of Automorphic Forms and the Trace Formula

2016-09-20 Mathematics
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Release : 2016-09-20
Genre : Mathematics
Kind : eBook
Book Rating : 240/5 ( reviews)

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Book Synopsis Families of Automorphic Forms and the Trace Formula by : Werner Müller

Download or read book Families of Automorphic Forms and the Trace Formula written by Werner Müller. This book was released on 2016-09-20. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on the Arthur-Selberg Trace Formula

1996 Mathematics
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Release : 1996
Genre : Mathematics
Kind : eBook
Book Rating : 711/5 ( reviews)

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Book Synopsis Lectures on the Arthur-Selberg Trace Formula by : Stephen S. Gelbart

Download or read book Lectures on the Arthur-Selberg Trace Formula written by Stephen S. Gelbart. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: 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).

A Local Relative Trace Formula for the Ginzburg-Rallis Model: The Geometric Side

2019-12-02 Education
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Release : 2019-12-02
Genre : Education
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Book Rating : 868/5 ( reviews)

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Book Synopsis A Local Relative Trace Formula for the Ginzburg-Rallis Model: The Geometric Side by : Chen Wan

Download or read book A Local Relative Trace Formula for the Ginzburg-Rallis Model: The Geometric Side written by Chen Wan. This book was released on 2019-12-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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