A01=Stephen S. Gelbart
Abelian extension
Abelian group
Additive group
Algebraic group
Algebraic number field
Algebraic number theory
Analytic continuation
Analytic function
Author_Stephen S. Gelbart
Automorphic form
Cartan subgroup
Category=PBF
Category=PBG
Congruence subgroup
Coprime integers
Cusp form
Differential equation
Dimension (vector space)
Direct integral
Division algebra
Eigenfunction
Eigenvalues and eigenvectors
Eisenstein series
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euler product
Exponential function
Factorization
Formal power series
Fourier series
Fuchsian group
Function (mathematics)
Function space
Functional equation
Fundamental unit (number theory)
Galois extension
Global field
Group algebra
Hecke L-function
Hilbert space
Induced representation
Infinite product
Inner automorphism
Invariant subspace
Irreducible representation
L-function
Lie algebra
Matrix coefficient
Mellin transform
Meromorphic function
Modular form
P-adic number
Poisson summation formula
Prime number
Principal series representation
Quadratic form
Quaternion algebra
Representation theory
Ring (mathematics)
Ring of integers
Selberg trace formula
Square-integrable function
Subgroup
Subquotient
Summation
Theorem
Theory
Theta function
Trace formula
Uniqueness theorem
Unitary operator
Unitary representation
Universal enveloping algebra
Variable (mathematics)
Weil group
Product details
- ISBN 9780691081564
- Weight: 397g
- Dimensions: 152 x 229mm
- Publication Date: 21 Mar 1975
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10.
Automorphic Forms on a Quaternion Algebra
