000			03445nam a22004218i 4500
001			CR9780511470905
003			UkCbUP
005			20200124160232.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090122s1995||||enk o ||1 0|eng|d
020			_a9780511470905 (ebook)
020			_z9780521418935 (hardback)
020			_z9780521070355 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA295 _b.M62 1995
082	0	0	_a515/.243 _220
100	1		_aMoeglin, Colette, _d1953- _eauthor.
245	1	0	_aSpectral decomposition and Eisenstein series : _bune paraphrase de l'écriture / _cC. Moeglin, J.-L. Waldspurger.
246	3		_aSpectral Decomposition & Eisenstein Series
264		1	_aCambridge : _bCambridge University Press, _c1995.
300			_a1 online resource (xxvii, 338 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v113
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aI. Hypotheses, automorphic forms, constant terms. I.1. Hypotheses and general notation. I.2. Automorphic forms: growth, constant terms. I.3. Cuspidal components. I.4. Upper bounds as functions of the constant term -- II. Decomposition according to cuspidal data. II. 1. Definitions. II. 2. Calculation of the scalar product of two pseudo-Eisenstein series -- III. Hilbertian operators and automorphic forms. III. 1. Hilbertian operators. III. 2. A decomposition of the space of automorphic forms. III. 3. Cuspidal exponents and square integrable automorphic forms -- IV. Continuation of Eisenstein series. IV. 1. The results. IV. 2. Some preparations. IV. 3. The case of relative rank 1. IV. 4. The general case -- V. Construction of the discrete spectrum via residues. V.1. Generalities and the residue theorem. V.2. Decomposition of the scalar product of two pseudo-Eisenstein series. V.3. Decomposition along the spectrum of the operators [Delta](f).
520			_aThe decomposition of the space L2(G(Q)\G(A)), where G is a reductive group defined over Q and A is the ring of adeles of Q, is a deep problem at the intersection of number and group theory. Langlands reduced this decomposition to that of the (smaller) spaces of cuspidal automorphic forms for certain subgroups of G. This book describes this proof in detail. The starting point is the theory of automorphic forms, which can also serve as a first step towards understanding the Arthur-Selberg trace formula. To make the book reasonably self-contained, the authors also provide essential background in subjects such as: automorphic forms; Eisenstein series; Eisenstein pseudo-series, and their properties. It is thus also an introduction, suitable for graduate students, to the theory of automorphic forms, the first written using contemporary terminology. It will be welcomed by number theorists, representation theorists and all whose work involves the Langlands program.
650		0	_aEisenstein series.
650		0	_aAutomorphic forms.
650		0	_aSpectral theory (Mathematics)
650		0	_aDecomposition (Mathematics)
700	1		_aWaldspurger, Jean-Loup, _d1953- _eauthor.
776	0	8	_iPrint version: _z9780521418935
830		0	_aCambridge tracts in mathematics ; _v113.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511470905
999			_c517761 _d517759