This graduate-level textbook presents an simple exposition of the speculation of automorphic representations and L-functions for the overall linear crew in an adelic surroundings. Definitions are stored to a minimal and repeated while reintroduced in order that the ebook is on the market from any access element, and without past wisdom of illustration idea. The publication contains concrete examples of world and native representations of GL(n), and offers their linked L-functions. In quantity 1, the speculation is constructed from first ideas for GL(1), then conscientiously prolonged to GL(2) with entire particular proofs of key theorems. a number of proofs are offered for the 1st time, together with Jacquet's easy and stylish facts of the tensor product theorem. In quantity 2, the better rank state of affairs of GL(n) is given an in depth remedy. Containing various routines, this publication will encourage scholars and researchers to start operating during this fertile box of study.
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