Automorphic Forms and RepresentationsThis book covers both the classical and representation theoretic views of automorphic forms in a style that is accessible to graduate students entering the field. The treatment is based on complete proofs, which reveal the uniqueness principles underlying the basic constructions. The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the Rankin-Selberg method and the triple L-function, and examines this subject matter from many different and complementary viewpoints. Researchers as well as students in algebra and number theory will find this a valuable guide to a notoriously difficult subject. |
Contents
V | 1 |
VI | 3 |
VII | 17 |
VIII | 26 |
IX | 41 |
X | 54 |
XI | 65 |
XII | 76 |
XXIX | 278 |
XXX | 291 |
XXXI | 307 |
XXXII | 321 |
XXXIII | 341 |
XXXIV | 346 |
XXXV | 368 |
XXXVI | 375 |
Common terms and phrases
a₁ adele ring admissible representation analytic continuation Archimedean assume automorphic forms automorphic representation coefficients commutative constant convergent cusp form cuspidal defined denote dimensional direct sum eigenvalues Eisenstein series element equals Exercise exists f₁ field finite finite-dimensional follows formula Fourier functional equation GL(n Haar measure Hecke character hence Hilbert space homomorphism identity integral invariant subspace irreducible admissible representation irreducible representations isomorphism Jacquet K-finite K)-module L-function Lē(G Langlands Lemma Let F Let G locally compact Ls(s Maass forms matrix meromorphic modular forms module multiple non-Archimedean nonramified nonzero notation operator poles Proposition prove quadratic quasicharacter re(s representation of G representation of GL(2 s₁ satisfying Eq Section side of Eq smooth spherical tensor Theorem topology unique unitary representation V₁ vector space w₁ Whittaker functional Whittaker model zero π₁ πο πυ χυ