By Dorian Goldfeld,Joseph Hundley

This graduate-level textbook presents an effortless exposition of the idea of automorphic representations and L-functions for the final linear crew in an adelic atmosphere. Definitions are saved to a minimal and repeated whilst reintroduced in order that the booklet is offered from any access element, and without previous wisdom of illustration thought. The e-book contains concrete examples of world and native representations of GL(n), and provides their linked L-functions. In quantity 1, the idea is built from first ideas for GL(1), then rigorously prolonged to GL(2) with whole special proofs of key theorems. a number of proofs are awarded for the 1st time, together with Jacquet's easy and chic evidence of the tensor product theorem. In quantity 2, the better rank state of affairs of GL(n) is given an in depth remedy. Containing a number of routines by means of Xander Faber, this publication will inspire scholars and researchers to start operating during this fertile box of research.

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