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Base Change For Gl 2
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Book Synopsis Base Change for GL(2) by : Robert P. Langlands
Download or read book Base Change for GL(2) written by Robert P. Langlands and published by Princeton University Press. This book was released on 1980-07-21 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. Langlands shows, in analogy with Artin's original treatment of one-dimensional p, that at least for tetrahedral p, L(s, p) is equal to the L-function L(s, π) attached to a cuspdidal automorphic representation of the group GL(2, /A), /A being the adéle ring of the field, and L(s, π), whose definition is ultimately due to Hecke, is known to be entire. The main result, from which the existence of π follows, is that it is always possible to transfer automorphic representations of GL(2) over one number field to representations over a cyclic extension of the field. The tools he employs here are the trace formula and harmonic analysis on the group GL(2) over a local field.
Book Synopsis Base Change for Gl(2) by : Robert P. Langlands
Download or read book Base Change for Gl(2) written by Robert P. Langlands and published by . This book was released on 1980 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Automorphic Forms and Representations by : Daniel Bump
Download or read book Automorphic Forms and Representations written by Daniel Bump and published by Cambridge University Press. This book was released on 1998-11-28 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes advanced graduate students from the foundations to topics on the research frontier.
Book Synopsis Derived Langlands: Monomial Resolutions Of Admissible Representations by : Victor P Snaith
Download or read book Derived Langlands: Monomial Resolutions Of Admissible Representations written by Victor P Snaith and published by World Scientific. This book was released on 2018-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally p-adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of distributions and representations of Hecke algebras. The monomial embedding, introduced in this book, elegantly fits together these two uses of distribution theory. The author follows up this application by giving the monomial category treatment of the Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.This book gives a new categorical setting in which to approach well-known topics. Therefore, the context used to explain examples is often the more generally accessible case of representations of finite general linear groups. For example, Galois base-change and epsilon factors for locally p-adic Lie groups are illustrated by the analogous Shintani descent and Kondo-Gauss sums, respectively. General linear groups of local fields are emphasized. However, since the philosophy of this book is essentially that of homotopy theory and algebraic topology, it includes a short appendix showing how the buildings of Bruhat-Tits, sufficient for the general linear group, may be generalised to the tom Dieck spaces (now known as the Baum-Connes spaces) when G is a locally p-adic Lie group.The purpose of this monograph is to describe a functorial embedding of the category of admissible k-representations of a locally profinite topological group G into the derived category of the additive category of the admissible k-monomial module category. Experts in the Langlands Programme may be interested to learn that when G is a locally p-adic Lie group, the monomial category is closely related to the category of topological modules over a sort of enlarged Hecke algebra with generators corresponding to characters on compact open modulo the centre subgroups of G. Having set up this functorial embedding, how the ingredients of the celebrated Langlands Programme adapt to the context of the derived monomial module category is examined. These include automorphic representations, epsilon factors and L-functions, modular forms, Weil-Deligne representations, Galois base change and Hecke operators.
Book Synopsis Automorphic Forms, Representations and $L$-Functions by : Armand Borel
Download or read book Automorphic Forms, Representations and $L$-Functions written by Armand Borel and published by American Mathematical Soc.. This book was released on 1979-06-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Book Synopsis The Abel Prize 2018-2022 by : Helge Holden
Download or read book The Abel Prize 2018-2022 written by Helge Holden and published by Springer Nature. This book was released on 2024 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the winners of the Abel Prize in mathematics for the period 2018-2022: - Robert P. Langlands (2018) - Karen K. Uhlenbeck (2019) - Hillel Furstenberg and Gregory Margulis (2020) - Lászlo Lóvász and Avi Wigderson (2021) - Dennis P. Sullivan (2022) The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos from the period 2018-2022 showing many of the additional activities connected with the Abel Prize. This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer, 2014) as well as on The Abel Prize 2013-2017 (Springer, 2019), which profile the previous Abel Prize laureates.
Book Synopsis Arithmetic and Geometry by : Luis Dieulefait
Download or read book Arithmetic and Geometry written by Luis Dieulefait and published by Cambridge University Press. This book was released on 2015-10-08 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1996-04 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operator Algebras, Operator Theory and Applications by : Maria Amélia Bastos
Download or read book Operator Algebras, Operator Theory and Applications written by Maria Amélia Bastos and published by Springer Science & Business Media. This book was released on 2008-05-27 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The book is aimed at postgraduates and researchers in these fields.
Book Synopsis Modular Forms and Fermat’s Last Theorem by : Gary Cornell
Download or read book Modular Forms and Fermat’s Last Theorem written by Gary Cornell and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.
Book Synopsis The Genesis of the Langlands Program by : Julia Mueller
Download or read book The Genesis of the Langlands Program written by Julia Mueller and published by Cambridge University Press. This book was released on 2021-08-05 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics.
Book Synopsis Number Theory and Its Applications in China by : Yuan Wang
Download or read book Number Theory and Its Applications in China written by Yuan Wang and published by American Mathematical Soc.. This book was released on 1988 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes the accomplishments of Chinese number theorists during 1949-1979, a period when correspondence between China and other countries was discouraged. This work presents a survey of the significant contributions of Chinese mathematicians. It also reflects the developments and state of research in number theory in China.
Book Synopsis Collected Works of Herve Jacquet by : Hervé Jacquet
Download or read book Collected Works of Herve Jacquet written by Hervé Jacquet and published by American Mathematical Soc.. This book was released on 2011 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Herve Jacquet is one of the founders of the modern theory of automorphic representations and their associated $L$-functions. This volume represents a selection of his most influential papers not already available in book form. The volume contains papers on the $L$-function attached to a pair of representations of the general linear group. Thus, it completes Jacquet's papers on the subject (joint with Shalika and Piatetski-Shapiro) that can be found in the volume of selected works of Piatetski-Shapiro. In particular, two often quoted papers of Jacquet and Shalika on the classification of automorphic representations and a historically important paper of Gelbart and Jacquet on the functorial transfer from $GL(2)$ to $GL(3)$ are included. Another series of papers pertains to the relative trace formula introduced by Jacquet. This is a variant of the standard trace formula which is used to study the period integrals of automorphic forms. Nearly complete results are obtained for the period of an automorphic form over a unitary group.
Book Synopsis Representation Theory and Automorphic Forms by : T. N. Bailey
Download or read book Representation Theory and Automorphic Forms written by T. N. Bailey and published by American Mathematical Soc.. This book was released on 1997 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Representation Theory and Number Theory in Connection with the Local Langlands Conjecture by : Jürgen Ritter
Download or read book Representation Theory and Number Theory in Connection with the Local Langlands Conjecture written by Jürgen Ritter and published by American Mathematical Soc.. This book was released on 1989 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langlands Program summarizes those parts of mathematical research belonging to the representation theory of reductive groups and to class field theory. These two topics are connected by the vision that, roughly speaking, the irreducible representations of the general linear group may well serve as parameters for the description of all number fields. In the local case, the base field is a given $p$-adic field $K$ and the extension theory of $K$ is seen as determined by the irreducible representations of the absolute Galois group $G_K$ of $K$. Great progress has been made in establishing correspondence between the supercuspidal representations of $GL(n,K)$ and those irreducible representations of $G_K$ whose degrees divide $n$. Despite these advances, no book or paper has presented the different methods used or even collected known results. This volume contains the proceedings of the conference ``Representation Theory and Number Theory in Connection with the Local Langlands Conjecture,'' held in December 1985 at the University of Augsburg. The program of the conference was divided into two parts: (i) the representation theory of local division algebras and local Galois groups, and the Langlands conjecture in the tame case; and (ii) new results, such as the case $n=p$, the matching theorem, principal orders, tame Deligne representations, classification of representations of $GL(n)$, and the numerical Langlands conjecture. The collection of papers in this volume provides an excellent account of the current state of the local Langlands Program.
Book Synopsis Number Theory, Trace Formulas and Discrete Groups by : Karl Egil Aubert
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.
Book Synopsis The Local Langlands Conjecture for GL(2) by : Colin J. Bushnell
Download or read book The Local Langlands Conjecture for GL(2) written by Colin J. Bushnell and published by Springer Science & Business Media. This book was released on 2006-08-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.
