Automorphic forms on SL₂(R)

by Armand Borel

Publisher: Cambridge University Press in Cambridge, U.K, New York, NY, USA

Written in English
Cover of: Automorphic forms on SL₂(R) | Armand Borel
Published: Pages: 192 Downloads: 139
Share This


  • Automorphic forms.

Edition Notes

Includes bibliographical references (p. 185-187) and indexes.

StatementArmand Borel.
SeriesCambridge tracts in mathematics ;, 130
LC ClassificationsQA331 .B687 1997
The Physical Object
Paginationx, 192 p. ;
Number of Pages192
ID Numbers
Open LibraryOL660636M
ISBN 100521580498
LC Control Number97006027

Classical automorphic forms and representations of SL(2) 2 (a) Φ(gk) = ε−m(k)Φ(g) for inSO2; (b) Rx+Φ = 0; (c) Φ(gz) = Φ(g) forz in the connected component of the center ofG. The existence of an automorphic form of weight m says something about the occurrence of a discrete series representation of G in C∞(Γ\G), but not quite what might be naively expected.   Abstract: This article describes a general method for computing automorphic forms using Voronoi-type summation formulas. It gives a numerical example where the technique is successful in quickly finding a cusp form on GL(3,Z)\GL(3,R), albeit one whose existence was already known as Author: Stephen D. Miller. Valentin Blomer: On the subconvexity problem for GL(3).; Siegfried Böcherer: On denominators of values of L-functions twisted by Dirichlet characters.; Kathrin Bringmann: Polar harmonic Maass forms.; YoungJu Choie: Period of modular forms on Γ 0 (N) and products of Jacobi theta functions.; Henri Darmon: p-adic modular forms of weight one and class fields of real quadratic fields. Armand Borel: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books.

2. Spectral correspondences for Maass forms 6 Chapter 2. Prerequisites 11 1. Fuchsian groups 11 2. Automorphic forms 13 3. The non-holomorphic Eisenstein series 14 4. The automorphic Laplacian 15 5. Modular symbols 18 Chapter 3. The distribution of modular symbols 21 1. Approximating cuspidal harmonic forms with compactly supported forms 21 2. In number theory, cuspidal representations are certain representations of algebraic groups that occur discretely in spaces. The term cuspidal is derived, at a certain distance, from the cusp forms of classical modular form theory. In the contemporary formulation of automorphic representations, representations take the place of holomorphic functions; these representations may be of adelic. In this book we focus on how to compute in practicethe spaces M k(N,ε) of modular forms, where k ≥ 2 is an integer and ε is a Dirichlet character of modulus N (the appendix treats modular forms for higher rank groups). We spend the most effort explaining the general algorithms that appear so far to be the best (in practice!) for such. Automorphic forms. Automorphic forms for congruence subgroups of SL_2(Z) and Hecke operators have very little to do with the above picture. Is the G-word-site clever enough to realise this? I think not but let's find out (26/11/09). Actually it turns out that it was. Let's try again (tinkered 11/11/10).

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable. Instanton Corrections to the Universal Hypermultiplet and Automorphic Fo rms on S U (2, 1) Ling Bao ♠, Axel Kleinschmidt ♦, Bengt E. W. Nilsson ♠, Daniel Persson ♠♦.

Automorphic forms on SL₂(R) by Armand Borel Download PDF EPUB FB2

Get this from a library. Automorphic forms on SL₂(R). [Armand Borel] -- Automorphic Forms on SL[subscript 2](R) provides an introduction to some aspects of the analytic theory of automorphic forms on G = SL[subscript 2](R) or the upper half-plane X, with respect to a. growth, etc.) are called automorphic forms on G.

Given an automorphic form f, roughly speaking, one considers the vector space V ˇ spanned by the space of functions g 7!f (gg 1) as g 1 varies over G and calls this the automorphic representation of G attached to f.

File Size: KB. Automorphic forms. [Anton Deitmar] This book provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. Modular forms for SL₂(Z) Representations of SL₂(R) p-Adic numbers Adeles and ideles Introductory lectures on automorphic forms Lectures for the European School of Group Theory July,Luminy, France by Nolan R.

Wallach 1 Orbital integrals and the Harish-Chandra transform. This section is devoted to a rapid review of some of the basic analysis that is necessary in representation theory and the basic theory of automorphic forms.

Eisenstein series and automorphic representations Philipp Fleig1, Henrik P. Gustafsson2, Axel Kleinschmidt3;4, Daniel Persson2 1Institut des Hautes Etudes Scienti ques, IHES Le Bois-Marie, 35, Route de Chartres, Bures-sur-Yvette, France 2Department of Physics, Chalmers University of Technology 96 Gothenburg, SwedenFile Size: 3MB.

This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making Cited by: AUTOMORPHIC FORMS ON GL 2 Introduction This is an introductory course to modular forms, automorphic forms and automorphic representations.

We will follow the plan outlined in a book of Bump [2] but also use materials from other sources as well. (1) Modular forms (2) Representations of GL 2(R) (3) Automorphic forms on GL 2(R) (4) Ad eles and id eles.

Automorphic Forms Online References This page is an incomplete, but evolving, list of some online references for learning about automorphic forms, representations and related topics.

It is focused on open-access notes and survey papers, not research papers. I may eventually add comments about each entry, and possibly will reorganize things by. 2 Automorphic representations and L-functions for GL(1,AQ)39 Automorphic forms for GL(1,AQ)39 The L-function of an automorphic form 45 The local L-functions and their functional equations 55 Classical L-functions and root numbers 60 Automorphic representations for GL(1,AQ)65 Hecke operators for GL(1,AQ) The Dimension of Spaces of Automorphic Forms* R.P.

Langlands 1. The trace formula of Selberg reduces the problem of calculating the dimension of a space of automorphic forms, at least when there is a compact fundamental domain, to the evaluation of certain integrals. Some of these integrals have been evaluated by Selberg.

This book is a course in representation theory of semisimple groups, automorphic forms, and the relations between these two subjects, written by some of the world's leading experts in these fields.

It is based on the instructional conference of the International Centre for Mathematical Sciences in Edinburgh. The book begins with an introductory treatment of structure theory and ends with. Corvallis proceedings. Ask Question Asked 8 years, 8 months ago.

Browse other questions tagged automorphic-forms -theory l-functions or ask your own question. Featured on Meta Improving the Review Queues - Project overview.

Introducing the Moderator Council - and its first, pro-tempore, representatives. In recent years, new and important connections have emerged between discrete subgroups of Lie groups, automorphic forms and arithmetic on the one hand, and questions in discrete mathematics, combinatorics, and graph theory on the other.

AUTOMORPHIC FORMS ON REDUCTIVE GROUPS ARMAND BOREL 1. Introduction The goal of these notes is the basic theory of automorphic forms and reductive groups, up to and including the analytic continuation of Eisenstein series.

Notation Let X be a. Abstract. One may view automorphic forms with general complex weight as functions on the upper half plane, or as functions on the universal covering group of SL 2 (ℝ).

In this book Author: Roelof W. Bruggeman. This year, the Automorphic Forms Workshop will be held in Moab, Utah at the Moab Arts and Recreation Center. Moab, in southern Utah, is near Arches and Canyonlands National Parks and other scenic landmarks.

The Workshop will be organized and hosted by Brigham Young University. Michael Harris Galois representations and automorphic forms. Deligne-Lusztig varieties More generally, if G is the group of F p-points of a reductive algebraic group (for example G = GL(n,F q) q = pr), then there is a family X w of Deligne-Lusztig varieties, with an action of G⇥TFile Size: KB.

Spaces of \(p\)-adic automorphic forms. Compute with harmonic cocycles and \(p\)-adic automorphic forms, including overconvergent \(p\)-adic automorphic forms. For a discussion of nearly rigid analytic modular forms and the rigid analytic Shimura-Maass operator, is worth also looking at for information on how these are implemented in this code.

automorphic forms on, or automorphic representations of, reductive groups, the local and global problems pertaining to them, and of their relations with the L- functions of algebraic number theory and algebraic geometry, such as Artin L.

Automorphic L-function, in mathematics; Automorphism, in mathematics; Rock microstructure#Crystal shapes; This disambiguation page lists articles associated with the title Automorphic. If an internal link led you here, you may wish to change the link to point directly to the.

An introduction to the theory of automorphic functions by Ford, Lester R., Publication date Topics Automorphic functions Publisher London G.

Bell Collection gerstein; toronto Digitizing sponsor MSN Contributor Gerstein - University of Toronto Language English. 14 Addeddate Bookplateleaf Pages: Automorphic forms on covering groups ofGL(2) Article (PDF Available) in Inventiones mathematicae 57(2) June with 73 Reads How we measure 'reads'Author: Yuval Flicker.

The inter-related study of motives and automorphic forms comprises some of the most central ideas and problems in number theory of our times. The arithmetic geometry of Diophantine equations eventually leads, following the well-known philosophy of Grothendieck, to the investigation of their constituent motives which, in turn, should be built from automorphic forms via the Langlands.

Automorphic forms on O s+2,2(R) and infinite products. Invent. Math. p. () Richard E. Borcherds. Mathematics department, University of California at Berkeley, CA U. e-mail: [email protected] 18 Augustcorrected 9 Dec. The denominator function of a generalized Kac-Moody algebra is often an automorphic.

One possible connection between T-functions and automorphic forms was established in [5] by using Poincar6 series. In this paper, we construct an element of an infinite-dimensional Grassmannian associated to an automorphic form using the Krichever : Min Ho Lee. Automorphic Forms, Mock Modular Forms and String Theory October 29 -- November 3,BIRS, Banff, Canada.

Functoriality and the Trace Formula December, The American Institute of Mathematics, San Jose, CA. Simons Symposium on Relative Trace Formulas April, (Schloss Elmau), Germany. THE2 DEFINITION OF AN AUTOMORPHIC REPRESENTATION (AND HOW TO GET ONE FROM A HOLOMORPHIC FORM) Definition.

If G is a topological group, then a unitary representation of G is an isometric action of G on a Hilbert space H so that the action map G £H!H is Size: KB. Automorphic forms onGL(2) 3 is a constituent of the space of automorphic forms. L (s,π C)) would then be, apart perhaps from a translation, the zeta-function L (s,C)of the π C is its own contragredient we would have L(s,C)= (s,π(C))L(1−s,C) and the factor (s,π(C)) = Πv (s,πv,ψv)could be computed in terms of local properties of the curve without reference to the theory of auto.

book [5]. Some other references are Bump’s book [2] and Jacquet’s book [3]. Bump’s book is easier to read but the real material is in [5]. Jacquet’s book develops theory of GL nautomorphic forms. Introduction and motivation This course will be about L-functions and automorphic forms.

There are two sorts of Size: KB. AUTOMORPHIC FORMS AND GALOIS REPRESENTATIONS TOM LOVERING Contents Introduction 2 1. Attaching Galois Representations to Modular Forms 4 The General Setup 5 The Shimura Isomorphism 6 Reduction mod p, and the Eichler-Shimura relation 8 Appendix: Good reduction of modular curves 12 Appendix: Weight 1 modular forms 12 2.

Multiple Dirichlet Series and Automorphic Forms Gautam Chinta, Solomon Friedberg, and Jeffrey Hoffstein Abstract. This article gives an introduction to the multiple Dirichlet series arising from sums of twisted automorphic L-functions.

We begin by explaining how such series arise from Rankin-Selberg constructions. Then more recent.ADDITIONAL REMARKS ON AUTOMORPHIC FORMS FOR 0(4) 3 ˇ 0ˇ 1ˇ 1=2 = 1. This is the sole relation between these generators, hence the group 0(4) is free on ˇ 0 and ˇ the character group _consists of the characters ; 0with (; 0) 2C2 mod Z2 given by () ˜File Size: KB.This conference aims to bring together leading experts in the vital area of automorphic forms and their L-functions, which enjoyed a lot of progress in the last couple of years.

A paradigmatic example for this development - to which the word "new directions" in the meeting's title alludes - is the Gan-Gross-Prasad conjecture (local and global).