Automorphic Representations Of Low Rank Groups
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Automorphic Representations Of Low Rank Groups
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Author : Yuval Zvi Flicker
language : en
Publisher: World Scientific
Release Date : 2006
Automorphic Representations Of Low Rank Groups written by Yuval Zvi Flicker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called OC liftingsOCO. This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E: F] = 2. The book develops the technique of comparison of twisted and stabilized trace formulae and considers the OC Fundamental LemmaOCO on orbital integrals of spherical functions. Comparison of trace formulae is simplified using OC regularOCO functions and the OC liftingOCO is stated and proved by means of character relations. This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, and a definition of packets for U(3), a proof of multiplicity one theorem and rigidity theorem for SL(2) and for U(3), a determination of the self-contragredient representations of PGL(3) and those on GL(3, E) fixed by transpose-inverse-bar. In particular, the multiplicity one theorem is new and recent. There are applications to construction of Galois representations by explicit decomposition of the cohomology of Shimura varieties of U(3) using Deligne''s (proven) conjecture on the fixed point formula. Sample Chapter(s). Chapter 1: Functoriality and Norms (963 KB). Contents: On the Symmetric Square Lifting: Functoriality and Norms; Orbital Integrals; Twisted Trace Formula; Total Global Comparison; Applications of a Trace Formula; Computation of a Twisted Character; Automorphic Representations of the Unitary Group U(3, E/F): Local Theory; Trace Formula; Liftings and Packets; Zeta Functions of Shimura Varieties of U(3): Automorphic Representations; Local Terms; Real Representations; Galois Representations. Readership: Graduate students and researchers in number theory, algebra and representation theory."
Automorphic Representations Of Low Rank Groups
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Author : Yuval Z Flicker
language : en
Publisher: World Scientific
Release Date : 2006-06-27
Automorphic Representations Of Low Rank Groups written by Yuval Z Flicker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-27 with Mathematics categories.
The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called “liftings”. This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E : F] = 2.The book develops the technique of comparison of twisted and stabilized trace formulae and considers the “Fundamental Lemma” on orbital integrals of spherical functions. Comparison of trace formulae is simplified using “regular” functions and the “lifting” is stated and proved by means of character relations.This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, and a definition of packets for U(3), a proof of multiplicity one theorem and rigidity theorem for SL(2) and for U(3), a determination of the self-contragredient representations of PGL(3) and those on GL(3, E) fixed by transpose-inverse-bar. In particular, the multiplicity one theorem is new and recent.There are applications to construction of Galois representations by explicit decomposition of the cohomology of Shimura varieties of U(3) using Deligne's (proven) conjecture on the fixed point formula.
Automorphic Representations Of Low Rank Groups
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Author : Yuval Z. Flicker
language : en
Publisher: Birkhauser
Release Date : 2004-12
Automorphic Representations Of Low Rank Groups written by Yuval Z. Flicker and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12 with Mathematics categories.
The area of automorphic representations and their local components (i.e. admissible representations) is a natural continuation of the main research of the 19th and 20th centuries studies in number theory and modular forms. A guiding principle is a reciprocity law that would relate these infinite-dimensional representations of a reductive group with finite dimensional representations of the Galois group of the number field.Simple relations on the Galois side would have deep counterpart relations on the automorphic side, called ''liftings''. These lifting relations are accessible purely on the automorphic side by using several analytic techniques. This monograph concentrates on one initial yet deep example, of the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of SL(2), namely its isomorphism with SO(3). It applies one technique, i.e. comparison of the trace formula with the twisted trace formula, both stabilized.All aspects of the technique are discussed in an elementary way:* The "Fundamental Lemma", relating orbital integrals of spherical functions;* Comparison of trace formulae is greatly simplified by using "regular" test functions;* The "lifting" is stated and proved by means of Harish-Chandra character relations.This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, proving the Multiplicity One Theorem and Rigidity Theorem for SL(2), as well as determining the self-contragredient representations of PGL(3).This research monograph will benefit an audience of graduate students and researchers in the areas of number theory, algebra, and representation theory.
Arthur S Invariant Trace Formula And Comparison Of Inner Forms
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Author : Yuval Z. Flicker
language : en
Publisher: Birkhäuser
Release Date : 2016-09-14
Arthur S Invariant Trace Formula And Comparison Of Inner Forms written by Yuval Z. Flicker and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-14 with Mathematics categories.
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 forms in general. Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur’s proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula. The final chapter illustrates the use of the formula by comparing it for G’ = GL(n) and its inner form G and for functions with matching orbital integrals.bribr/i/idiviiArthur’s Invariant Trace Formula and Comparison of Inner Forms/div
The Descent Map From Automorphic Representations Of Gl N To Classical Groups
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Author : David Ginzburg
language : en
Publisher: World Scientific
Release Date : 2011
The Descent Map From Automorphic Representations Of Gl N To Classical Groups written by David Ginzburg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of the Gelfand?Graev type, or of the Fourier?Jacobi type to certain residual Eisenstein series. An account of this automorphic descent, with complete, detailed proofs, leads to a thorough understanding of important ideas and techniques. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively self-contained, the content of some of the chapters can serve as topics for graduate students seminars.
Computations With Modular Forms
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Author : Gebhard Böckle
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-23
Computations With Modular Forms written by Gebhard Böckle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-23 with Mathematics categories.
This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.
Eisenstein Series And Automorphic Representations
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Author : Philipp Fleig
language : en
Publisher: Cambridge Studies in Advanced
Release Date : 2018-07-05
Eisenstein Series And Automorphic Representations written by Philipp Fleig and has been published by Cambridge Studies in Advanced this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-05 with Mathematics categories.
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Automorphic Representations L Functions And Applications Progress And Prospects
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Author : James W. Cogdell
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Automorphic Representations L Functions And Applications Progress And Prospects written by James W. Cogdell 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 2011-06-24 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, Mœglin, 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.
Automorphic Forms And L Functions I
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Author : David Ginzburg
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Automorphic Forms And L Functions I written by David Ginzburg 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 2009 with Mathematics categories.
Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.
First International Congress Of Chinese Mathematicians
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Author : Stephen Shing-Toung Yau
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
First International Congress Of Chinese Mathematicians written by Stephen Shing-Toung Yau 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 2001 with Mathematics categories.
The International Congress of Mathematicians was an historical event that was held at the Morningside Center of Mathematics of the Chinese Academy of Sciences (Beijing). It was the first occasion where Chinese mathematicians from all over the world gathered to present their research. The Morningside Mathematics lectures were given by R. Borcherds, J. Coates, R. Graham, and D. Stroock. Other distinguished speakers included J.-P. Bourguignon, J. Jöst, M. Taylor, and S. L. Lee. Topics covered in the volume include algebra and representation theory, algebraic geometry, number theory and automorphic forms, Riemannian geometry and geometric analysis, mathematical physics, topology, complex analysis and complex geometry, computational mathematics, and combinatorics. Titles in this series are copublished with International Press, Cambridge, MA.