000 04180nam a22004815i 4500
001 978-3-540-46659-8
003 DE-He213
005 20190213151453.0
007 cr nn 008mamaa
008 121227s1992 gw | s |||| 0|eng d
020 _a9783540466598
_9978-3-540-46659-8
024 7 _a10.1007/BFb0092305
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
_2thema
082 0 4 _a512.7
_223
100 1 _aShokranian, Salahoddin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Selberg-Arthur Trace Formula
_h[electronic resource] :
_bBased on Lectures by James Arthur /
_cby Salahoddin Shokranian.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1992.
300 _aIX, 99 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1503
505 0 _aContents: Number Theory and Automorphic Representations: Some problems in classical number theory. Modular forms and automorphic representations -- Selberg's Trace Formula: Historical Remarks. Orbital integrals and Selberg's trace formula. Three examples. A necessary condition. Generalizations and applications -- Kernel Functions and the Convergence Theorem: Preliminaries on GL(r). Combinatorics and reduction theory. The convergence theorem -- The Adélic Theory: Basic facts -- The Geometric Theory: The JTO(f) and JT(f) distributions. A geometric I-function. The weight functions -- The Geometric Expansion of the Trace Formula: Weighted orbital integrals. The unipotent distribution -- The Spectral Theory: A review of the Eisenstein series. Cusp forms, truncation, the trace formula -- The Invariant Trace Formula and Its Applications: The in- variant trace formula for GL(r). Applications and remarks -- Bibliography -- Subject Index.
520 _aThis book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks.
650 0 _aNumber theory.
650 0 _aTopological Groups.
650 1 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662173039
776 0 8 _iPrinted edition:
_z9783540550211
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1503
856 4 0 _uhttps://doi.org/10.1007/BFb0092305
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10785
_d10785