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Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120

Laurent Clozel, James Arthur

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

A 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.

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Schlagwörter

Summation, Algebraic group, Binomial coefficient, Unitary representation, Poisson summation formula, Cartan subalgebra, Spherical harmonics, Maximal compact subgroup, Finite set, Lie algebra, Characteristic polynomial, Algebraic number field, Diagram (category theory), Mathematical induction, Root of unity, Support (mathematics), Irreducibility (mathematics), Cusp form, Identity component, Nilpotent group, Galois group, Harmonic analysis, P-adic number, Automorphism, Scientific notation, Galois extension, Trace formula, Eisenstein series, Existential quantification, Fundamental lemma (Langlands program), L-function, Admissible representation, Langlands classification, Hilbert's Theorem 90, Laurent series, Base change, Orbital integral, Invariant measure, Coxeter element, Division algebra, Infinite product, Linear algebraic group, Induced representation, Grothendieck group, Irreducible representation, Central simple algebra, Reciprocal lattice, Global field, Exact sequence, Theorem, Archimedean property, Reductive group, Weil group, Subgroup, Fourier transform, Special case, Tensor product, Computation, Determinant, Weyl group, Automorphic form, Cyclic permutation, Canonical map, Haar measure, Hecke algebra, Conjugacy class, Paley–Wiener theorem, Big O notation, Density theorem, Discrete series representation