Base Change for GL(2). (AM-96), Volume 96 (Annals of Mathematics Studies, 96) by Robert P. Langlands (PDF)

Description

R. Langlands shows, in analogy with Artin’s original treatment of one-dimensional p, that at least for tetrahedral p, L(s, p) is equal to the L-function L(s, π) attached to a cuspdidal automorphic representation of the group GL(2, /A), /A being the adéle ring of the field, and L(s, π), whose definition is ultimately due to Hecke, is known to be entire. The main result, from which the existence of π follows, is that it is always possible to transfer automorphic representations of GL(2) over one number field to representations over a cyclic extension of the field. The tools he employs here are the trace formula and harmonic analysis on the group GL(2) over a local field.

User’s Reviews

Editorial Reviews: From the Back Cover The problem of base change or of lifting for automorphic representations can be introduced in several ways. It emerges very quickly when one pursues the formal principles expounded in the article 20 which can in fact be reduced to one, viz., the functoriality of automorphic forms with respect to what is now referred as the L-group.

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