By Stephen S. Gelbart
This quantity investigates the interaction among the classical conception of automorphic types and the fashionable concept of representations of adele teams. examining vital fresh contributions of Jacquet and Langlands, the writer offers new and formerly inaccessible effects, and systematically develops specific outcomes and connections with the classical idea. The underlying subject is the decomposition of the commonplace illustration of the adele staff of GL(2). an in depth facts of the distinguished hint formulation of Selberg is incorporated, with a dialogue of the potential diversity of applicability of this formulation. in the course of the paintings the writer emphasizes new examples and difficulties that stay open in the basic theory.
TABLE OF CONTENTS: 1. The Classical idea 2. Automorphic kinds and the Decomposition of L2(PSL(2,R) three. Automorphic kinds as capabilities at the Adele workforce of GL(2) four. The Representations of GL(2) over neighborhood and international Fields five. Cusp varieties and Representations of the Adele staff of GL(2) 6. Hecke concept for GL(2) 7. the development of a unique type of Automorphic types eight. Eisenstein sequence and the continual Spectrum nine. The hint formulation for GL(2) 10. Automorphic varieties on a Quaternion Algebra
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