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035   $a(OCoLC)979580917
035   $a(DE-B1597)9781400882403
035   $a(EXLCZ)993710000000631380
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aSimple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120 /$fLaurent Clozel, James Arthur
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1989
215   $a1 online resource (248 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v351
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08517-X 
311   $a0-691-08518-8 
320   $aBibliography.
327   $tFrontmatter -- $tContents -- $tIntroduction -- $tChapter 1. Local Results -- $tChapter 2. The Global Comparison -- $tChapter 3. Base Change -- $tBibliography
330   $aA general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.
410  0$aAnnals of mathematics studies ;$vno. 120.
606   $aRepresentations of groups
606   $aTrace formulas
606   $aAutomorphic forms
610   $a0E.
610   $aAddition.
610   $aAdmissible representation.
610   $aAlgebraic group.
610   $aAlgebraic number field.
610   $aApproximation.
610   $aArchimedean property.
610   $aAutomorphic form.
610   $aAutomorphism.
610   $aBase change.
610   $aBig O notation.
610   $aBinomial coefficient.
610   $aCanonical map.
610   $aCartan subalgebra.
610   $aCartan subgroup.
610   $aCentral simple algebra.
610   $aCharacteristic polynomial.
610   $aClosure (mathematics).
610   $aCombination.
610   $aComputation.
610   $aConjecture.
610   $aConjugacy class.
610   $aConnected component (graph theory).
610   $aContinuous function.
610   $aContradiction.
610   $aCorollary.
610   $aCounting.
610   $aCoxeter element.
610   $aCusp form.
610   $aCyclic permutation.
610   $aDense set.
610   $aDensity theorem.
610   $aDeterminant.
610   $aDiagram (category theory).
610   $aDiscrete series representation.
610   $aDiscrete spectrum.
610   $aDivision algebra.
610   $aEigenvalues and eigenvectors.
610   $aEisenstein series.
610   $aExact sequence.
610   $aExistential quantification.
610   $aField extension.
610   $aFinite group.
610   $aFinite set.
610   $aFourier transform.
610   $aFunctor.
610   $aFundamental lemma (Langlands program).
610   $aGalois extension.
610   $aGalois group.
610   $aGlobal field.
610   $aGrothendieck group.
610   $aGroup representation.
610   $aHaar measure.
610   $aHarmonic analysis.
610   $aHecke algebra.
610   $aHilbert's Theorem 90.
610   $aIdentity component.
610   $aInduced representation.
610   $aInfinite product.
610   $aInfinitesimal character.
610   $aInvariant measure.
610   $aIrreducibility (mathematics).
610   $aIrreducible representation.
610   $aL-function.
610   $aLanglands classification.
610   $aLaurent series.
610   $aLie algebra.
610   $aLie group.
610   $aLinear algebraic group.
610   $aLocal field.
610   $aMathematical induction.
610   $aMaximal compact subgroup.
610   $aMultiplicative group.
610   $aNilpotent group.
610   $aOrbital integral.
610   $aP-adic number.
610   $aPaley?Wiener theorem.
610   $aParameter.
610   $aParametrization.
610   $aPermutation.
610   $aPoisson summation formula.
610   $aReal number.
610   $aReciprocal lattice.
610   $aReductive group.
610   $aRoot of unity.
610   $aScientific notation.
610   $aSemidirect product.
610   $aSpecial case.
610   $aSpherical harmonics.
610   $aSubgroup.
610   $aSubset.
610   $aSummation.
610   $aSupport (mathematics).
610   $aTensor product.
610   $aTheorem.
610   $aTrace formula.
610   $aUnitary representation.
610   $aWeil group.
610   $aWeyl group.
610   $aZero of a function.
615  0$aRepresentations of groups.
615  0$aTrace formulas.
615  0$aAutomorphic forms.
676   $a512/.2
686   $aSK 240$2rvk
700   $aArthur$b James, $0348301
702   $aClozel$b Laurent, 
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154743703321
996   $aSimple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120$92571941
997   $aUNINA