Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula
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A01=James Arthur
A01=Laurent Clozel
Admissible representation
Algebraic group
Algebraic number field
Archimedean property
Author_James Arthur
Author_Laurent Clozel
Automorphic form
Automorphism
Base change
Big O notation
Binomial coefficient
Canonical map
Cartan subalgebra
Category=PBG
Central simple algebra
Characteristic polynomial
Computation
Conjugacy class
Coxeter element
Cusp form
Cyclic permutation
Density theorem
Determinant
Diagram (category theory)
Discrete series representation
Division algebra
Eisenstein series
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exact sequence
Existential quantification
Finite set
Fourier transform
Fundamental lemma (Langlands program)
Galois extension
Galois group
Global field
Grothendieck group
Haar measure
Harmonic analysis
Hecke algebra
Hilbert's Theorem 90
Identity component
Induced representation
Infinite product
Invariant measure
Irreducibility (mathematics)
Irreducible representation
L-function
Langlands classification
Laurent series
Lie algebra
Linear algebraic group
Mathematical induction
Maximal compact subgroup
Nilpotent group
Orbital integral
P-adic number
Paley-Wiener theorem
Poisson summation formula
Reciprocal lattice
Reductive group
Root of unity
Scientific notation
Special case
Spherical harmonics
Subgroup
Summation
Support (mathematics)
Tensor product
Theorem
Trace formula
Unitary representation
Weil group
Weyl group
Product details
- ISBN 9780691085180
- Weight: 369g
- Dimensions: 152 x 229mm
- Publication Date: 21 Jun 1989
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
