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BOOK EXCERPT:
This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
Product Details :
Genre |
: Mathematics |
Author |
: Joseph Bernstein |
Publisher |
: Springer Science & Business Media |
Release |
: 2013-12-11 |
File |
: 283 Pages |
ISBN-13 |
: 9780817682262 |
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BOOK EXCERPT:
A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.
Product Details :
Genre |
: Mathematics |
Author |
: Julia Mueller |
Publisher |
: Cambridge University Press |
Release |
: 2021-08-05 |
File |
: 451 Pages |
ISBN-13 |
: 9781108710947 |
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BOOK EXCERPT:
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
Product Details :
Genre |
: Mathematics |
Author |
: Caterina Consani |
Publisher |
: Springer Science & Business Media |
Release |
: 2007-12-18 |
File |
: 374 Pages |
ISBN-13 |
: 9783834803528 |
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BOOK EXCERPT:
This is a collection of lecture notes from the minicourses in the December 2018 Langlands Workshop: Endoscopy and Beyond. The volume combines seven introductory chapters on trace formulas, local Arthur packets, and beyond endoscopy. It aims to introduce the endoscopy classification via a basic example of the trace formula for SL(2), explore the more refined questions on the structure of Arthur packets, and look beyond endoscopy following the suggestions of Langlands, Braverman-Kazhdan, Ngo, and Altuğ. The book is a helpful reference for undergraduates, postgraduates, and researchers.
Product Details :
Genre |
: Mathematics |
Author |
: Wee Teck Gan |
Publisher |
: World Scientific |
Release |
: 2024-04-15 |
File |
: 449 Pages |
ISBN-13 |
: 9789811285837 |
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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
Product Details :
Genre |
: Mathematics |
Author |
: T. N. Bailey |
Publisher |
: American Mathematical Soc. |
Release |
: 1997 |
File |
: 490 Pages |
ISBN-13 |
: 9780821806098 |
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BOOK EXCERPT:
Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.
Product Details :
Genre |
: Mathematics |
Author |
: Ian Hacking |
Publisher |
: Cambridge University Press |
Release |
: 2014-01-30 |
File |
: 307 Pages |
ISBN-13 |
: 9781107050174 |
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BOOK EXCERPT:
This collection of essays spans pure and applied mathematics. Readers interested in mathematical research and historical aspects of mathematics will appreciate the enlightening content of the material. Highlighting the pervasive nature of mathematics today in a host of different areas, the book also covers the spread of mathematical ideas and techn
Product Details :
Genre |
: Mathematics |
Author |
: R. Sujatha |
Publisher |
: CRC Press |
Release |
: 2011-11-11 |
File |
: 488 Pages |
ISBN-13 |
: 9781439876336 |
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BOOK EXCERPT:
James W. Cogdell, Lectures on $L$-functions, converse theorems, and functoriality for $GL_n$: Preface Modular forms and their $L$-functions Automorphic forms Automorphic representations Fourier expansions and multiplicity one theorems Eulerian integral representations Local $L$-functions: The non-Archimedean case The unramified calculation Local $L$-functions: The Archimedean case Global $L$-functions Converse theorems Functoriality Functoriality for the classical groups Functoriality for the classical groups, II Henry H. Kim, Automorphic $L$-functions: Introduction Chevalley groups and their properties Cuspidal representations $L$-groups and automorphic $L$-functions Induced representations Eisenstein series and constant terms $L$-functions in the constant terms Meromorphic continuation of $L$-functions Generic representations and their Whittaker models Local coefficients and non-constant terms Local Langlands correspondence Local $L$-functions and functional equations Normalization of intertwining operators Holomorphy and bounded in vertical strips Langlands functoriality conjecture Converse theorem of Cogdell and Piatetski-Shapiro Functoriality of the symmetric cube Functoriality of the symmetric fourth Bibliography M. Ram Murty, Applications of symmetric power $L$-functions: Preface The Sato-Tate conjecture Maass wave forms The Rankin-Selberg method Oscillations of Fourier coefficients of cusp forms Poincare series Kloosterman sums and Selberg's conjecture Refined estimates for Fourier coefficients of cusp forms Twisting and averaging of $L$-series The Kim-Sarnak theorem Introduction to Artin $L$-functions Zeros and poles of Artin $L$-functions The Langlands-Tunnell theorem Bibliography
Product Details :
Genre |
: Mathematics |
Author |
: James W. Cogdell |
Publisher |
: American Mathematical Soc. |
Release |
: |
File |
: 300 Pages |
ISBN-13 |
: 082187179X |
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BOOK EXCERPT:
These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.
Product Details :
Genre |
: Mathematics |
Author |
: Jr̲n Steuding |
Publisher |
: Springer Science & Business Media |
Release |
: 2007-06-06 |
File |
: 320 Pages |
ISBN-13 |
: 9783540265269 |
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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.
Product Details :
Genre |
: Mathematics |
Author |
: Victor P Snaith |
Publisher |
: World Scientific |
Release |
: 2018-12-06 |
File |
: 356 Pages |
ISBN-13 |
: 9789813275768 |