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Automorphic representations and L-functions for the general linear group. Volume I /
This modern, graduate-level textbook does not assume prior knowledge of representation theory. Includes numerous concrete examples and over 250 exercises.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2011.
|
| Colección: | Cambridge studies in advanced mathematics ;
129. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Goldfeld, D. | |
| 245 | 1 | 0 | |a Automorphic representations and L-functions for the general linear group. |n Volume I / |c Dorian Goldfeld, Joseph Hundley ; with exercises by Xander Faber. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (xix, 550 pages). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics ; |v 129 | |
| 504 | |a Includes bibliographical references (pages 531-536) and indexes. | ||
| 505 | 0 | |a Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents for Volume I -- Contents for Volume II -- Introduction -- Preface to the Exercises -- 1 Adeles over Q -- 1.1 Absolute values -- 1.2 The field Qp of p-adic numbers -- 1.3 Adeles and ideles over Q -- 1.4 Action of Q on the adeles and ideles -- 1.5 p-adic integration -- 1.6 p-adic Fourier transform -- 1.7 Adelic Fourier transform -- 1.8 Fourier expansion of periodic adelic functions -- 1.9 Adelic Poisson summation formula -- Exercises for Chapter 1 -- 2 Automorphic representations and L-functions for GL(1, AQ) -- 2.1 Automorphic forms for GL (1, AQ) -- 2.2 The L-function of an automorphic form -- 2.3 The local L-functions and their functional equations -- 2.4 Classical L-functions and root numbers -- 2.5 Automorphic representations for GL(1, AQ) -- 2.6 Hecke operators for GL(1, AQ) -- 2.7 The Rankin-Selberg method -- 2.8 The p-adic Mellin transform -- Exercises for Chapter 2 -- 3 The classical theory of automorphic forms for GL(2) -- 3.1 Automorphic forms in general -- 3.2 Congruence subgroups of the modular group -- 3.3 Automorphic functions of integral weight k -- 3.4 Fourier expansion at ... of holomorphic modular forms -- 3.5 Maass forms -- 3.6 Whittaker functions -- 3.7 Fourier-Whittaker expansions of Maass forms -- 3.8 Eisenstein series -- 3.9 Maass raising and lowering operators -- 3.10 The bottom of the spectrum -- 3.11 Hecke operators, oldforms, and newforms -- 3.12 Finite dimensionality of the eigenspaces -- Exercises for Chapter 3 -- 4 Automorphic forms for GL(2, AQ) -- 4.1 Iwasawa and Cartan decompositions for GL(2, R) -- 4.2 Iwasawa and Cartan decompositions for GL(2, Qp) -- 4.3 The adele group GL(2, AQ) -- 4.4 The action of GL (2, Q) on GL(2, AQ) -- 4.5 The universal enveloping algebra of gl(2,C). | |
| 505 | 8 | |a 4.6 The center of the universal enveloping algebra of gl(2, C) -- 4.7 Automorphic forms for GL(2, AQ) -- 4.8 Adelic lifts of weight zero, level one, Maass forms -- 4.9 The Fourier expansion of adelic automorphic forms -- 4.10 Global Whittaker functions for GL(2, AQ) -- 4.11 Strong approximation for congruence subgroups -- 4.12 Adelic lifts with arbitrary weight, level, and character -- 4.13 Global Whittaker functions for adelic lifts with arbitrary weight, level, and character -- Exercises for Chapter 4 -- 5 Automorphic representations for GL(2, AQ) -- 5.1 Adelic automorphic representations for GL(2, AQ) -- 5.2 Explicit realization of actions defining a (g, K ...)-module -- 5.3 Explicit realization of the action of GL(2, Afinite) -- 5.4 Examples of cuspidal automorphic representations -- 5.5 Admissible (g, K ...) × GL(2, Afinite)-modules -- Exercises for Chapter 5 -- 6 Theory of admissible representations of GL(2, Qp) -- 6.0 Short roadmap to chapter 6 -- 6.1 Admissible representations of GL(2, Qp) -- 6.2 Ramified versus unramified -- 6.3 Local representation coming from a level 1 Maass form -- 6.4 Jacquet's local Whittaker function -- 6.5 Principal series representations -- 6.6 Jacquet's map: Principal series larrow Whittaker functions -- 6.7 The Kirillov model -- 6.8 The Kirillov model of the principal series representation -- 6.9 Haar measure on GL(2, Qp) -- 6.10 The special representations -- 6.11 Jacquet modules -- 6.12 Induced representations and parabolic induction -- 6.13 The supercuspidal representations of GL(2, Qp) -- 6.14 The uniqueness of the Kirillov model -- 6.15 The Kirillov model of a supercuspidal representation -- 6.16 The classification of the irreducible and admissible representations of GL(2, Qp) -- Exercises for Chapter 6 -- 7 Theory of admissible (g, K8) modules for GL(2, R) -- 7.1 Admissible (g, K8)-modules. | |
| 505 | 8 | |a 7.2 Ramified versus unramified -- 7.3 Jacquet's local Whittaker function -- 7.4 Principal series representations -- 7.5 Classification of irreducible admissible (g, K8)-modules -- Exercises for Chapter 7 -- 8 The contragredient representation for GL(2) -- 8.1 The contragredient representation for GL(2, Qp) -- 8.2 The contragredient representation of a principal series representation of GL(2, Qp) -- 8.3 Contragredient of a special representation of GL(2, Qp) -- 8.4 Contragredient of a supercuspidal representation -- 8.5 The contragredient representation for GL(2, R) -- 8.6 The contragredient representation of a principal series representation of GL(2, R) -- 8.7 Global contragredients for GL(2, AQ) -- 8.8 Integration on GL(2, AQ) -- 8.9 The contragredient representation of a cuspidal automorphic representation of GL(2, AQ) -- 8.10 Growth of matrix coefficients -- 8.11 Asymptotics of matrix coefficients of (g, K8)-modules -- 8.12 Matrix coefficients of GL(2, Qp) via the Jacquet module -- Exercises for Chapter 8 -- 9 Unitary representations of GL (2) -- 9.1 Unitary representations of GL(2, Qp) -- 9.2 Unitary principal series representations of GL(2, Qp) -- 9.3 Unitary and irreducible special or supercuspidal representations of GL(2, Qp) -- 9.4 Unitary (g, K8)-modules -- 9.5 Unitary (g, K8) × GL(2,Afinite)-modules -- Exercises for Chapter 9 -- 10 Tensor products of local representations -- 10.1 Euler products -- 10.2 Tensor product of (g, K8)-modules and representations -- 10.3 Infinite tensor products of local representations -- 10.4 The factorization of unramified irreducible admissible cuspidal automorphic representations -- 10.5 Decomposition of representations of locally compact groups into finite tensor products -- 10.6 The spherical Hecke algebra for GL(2, Qp) -- 10.7 Initial decomposition of admissible (g, K8) × GL(2,Afinite)-modules. | |
| 505 | 8 | |a 10.8 The tensor product theorem -- 10.9 The Ramanujan and Selberg conjectures for GL(2, AQ) -- Exercises for Chapter 10 -- 11 The Godement-Jacquet L-function for GL(2, AQ) -- 11.1 Historical remarks -- 11.2 The Poisson summation formula for GL(2, AQ) -- 11.3 Haar measure -- 11.4 The global zeta integral for GL(2, AQ) -- 11.5 Factorization of the global zeta integral -- 11.6 The local functional equation -- 11.7 The local L-function for GL(2, Qp) (unramified case) -- 11.8 The local L-function for irreducible supercuspidal representations of GL(2, Qp) -- 11.9 The local L-function for irreducible principal series representations of GL(2, Qp) -- 11.10 Local L-function for unitary special representations of GL(2, Qp) -- 11.11 Proof of the local functional equation for principal series representations of GL(2, Qp) -- 11.12 The local functional equation for the unitary special representations of GL(2, Qp) -- 11.13 Proof of the local functional equation for the supercuspidal representations of GL(2, Qp) -- 11.14 The local L-function for irreducible principal series representations of GL(2, R) -- 11.15 Proof of the local functional equation for principal series representations of GL(2, R) -- 11.16 The local L-function for irreducible discrete series representations of GL(2, R) -- Exercises for Chapter 11 -- Solutions to Selected Exercises -- References -- Symbols Index -- Index. | |
| 520 | |a This modern, graduate-level textbook does not assume prior knowledge of representation theory. Includes numerous concrete examples and over 250 exercises. | ||
| 588 | |a Description based on online resource; title from digital title page (viewed on January 24, 2020). | ||
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Automorphic forms. | |
| 650 | 0 | |a L-functions. | |
| 650 | 0 | |a Representations of groups. | |
| 650 | 6 | |a Formes automorphes. | |
| 650 | 6 | |a Fonctions L. | |
| 650 | 6 | |a Représentations de groupes. | |
| 650 | 7 | |a MATHEMATICS |x Complex Analysis. |2 bisacsh | |
| 650 | 7 | |a Automorphic forms |2 fast | |
| 650 | 7 | |a L-functions |2 fast | |
| 650 | 7 | |a Representations of groups |2 fast | |
| 700 | 1 | |a Hundley, Joseph. | |
| 776 | 0 | 8 | |i Print version: |a Goldfeld, D. |t Automorphic representations and L-functions for the general linear group. Vol. 1. |d Cambridge : Cambridge University Press, 2011 |z 9780521474238 |w (OCoLC)665137577 |
| 830 | 0 | |a Cambridge studies in advanced mathematics ; |v 129. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=366233 |z Texto completo |
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