Download or read book Relative Trace Formulas written by Werner Müller and published by Springer Nature. This book was released on 2021-05-18 with total page 438 pages. 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.

Download or read book On the Local Relative Trace Formula written by Jonathan Sparling and published by . This book was released on 2009 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lectures on the Arthur Selberg Trace Formula written by Stephen S. Gelbart and published by American Mathematical Soc.. This book was released on 1996 with total page 112 pages. 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).

Download or read book A Local Relative Trace Formula for the Ginzburg Rallis Model The Geometric Side written by Chen Wan and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 90 pages. 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.

Download or read book Families of Automorphic Forms and the Trace Formula written by Werner Müller and published by Springer. This book was released on 2016-09-20 with total page 581 pages. 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.

Download or read book On the Spectral Expansion of a Relative Trace Formula written by K. F. Lai and published by . This book was released on 1992 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Periods and Relative Trace Formulas for GL 2 in the Local Setting written by Brooke Gabrielle Feigon and published by . This book was released on 2006 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: By comparing the relative and Kuznetsov trace formulas in the global setting, Jacquet developed a method for characterizing the image of the base change map associating automorphic representations of U(2, AE/AF) to automorphic representations of GL(2, A E). Here we define, prove and compare local versions of the relative and Kuznetsov trace formulas on GL(2) and U(2). When evaluated with matching functions, the local Kuznetsov trace formula and the local relative trace formula are equal and thus there is an equality between their local distributions on the spectral sides. To define the local distributions for the relative trace formula, we define a regularized period integral and prove that it is a GL(2, F) invariant linear functional.

Download or read book Contributions to the Relative Trace Formula of Guo Jacquet written by Huajie Li and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Relative Trace Formula for SO2 SO3 and the Waldspurger Formula written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We provide a new relative trace formula approach to the theorem of Waldspurger on toric periods for GL2, with possible applications to the global Gross-Prasad conjecture for orthogonal groups.

Download or read book Number Theory Trace Formulas and Discrete Groups written by Karl Egil Aubert and published by Academic Press. This book was released on 2014-05-10 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Geometric Aspects of the Trace Formula written by Werner Müller and published by Springer. This book was released on 2018-10-11 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Local Relative Trace Formula for Spherical Varieties written by Ioan Filip and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Let F be a local non-Archimedean field of characteristic zero. We prove a Plancherel formula for the symmetric space GL(2,F)\GL(2,E), where E/F is an unramified quadratic extension. Our method relies on intrinsic geometric and combinatorial properties of spherical varieties and constitutes the local counterpart of the global computation of the Flicker-Rallis period as a residue of periods against Eisenstein series. We also give a novel derivation of the Plancherel formula for the strongly tempered variety T\PGL(2) over F (with maximal split torus T) using a canonical smooth asymptotics morphism and a contour shifting method. In this rank one local setting, our proof is similar to Langlands' proof over global fields describing the spectrum of a reductive group in terms of residues of Eisenstein series. Finally, using both L2-decompositions, we develop a local relative trace formula and outline a comparison result in the setting of the unitary rank one Gan-Gross-Prasad conjecture.

Download or read book Local Analysis of Selberg s Trace Formula written by A. Good and published by . This book was released on 2014-01-15 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Central Critical Values of the Degree Four L Functions for GSp 4 The Fundamental Lemma III written by Masaaki Furusawa and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four -functions for , and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.

Download or read book Kuznetsov s Trace Formula and the Hecke Eigenvalues of Maass Forms written by Andrew Knightly and published by American Mathematical Soc.. This book was released on 2013-06-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.

Download or read book Kuznetsov s Trace Formula and the Hecke Eigenvalues of Maass Forms written by Andrew Knightly and published by . This book was released on 2013 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Stabilization of the Trace Formula written by Laurent Clozel and published by International Pressof Boston Incorporated. This book was released on 2011 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: