000 | 04180nam a22004815i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/BFb0092305 _2doi |
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050 | 4 | _aQA241-247.5 | |
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_aPBH _2bicssc |
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_aMAT022000 _2bisacsh |
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_aPBH _2thema |
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082 | 0 | 4 |
_a512.7 _223 |
100 | 1 |
_aShokranian, Salahoddin. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aIX, 99 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1503 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0092305 |
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