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Base change for GL(2)

by Robert P. Langlands

(Annals of mathematics studies, no. 96)(Tokyo University international edition, no. 172)

Princeton University Press , University of Tokyo Press, 1980

  • : hbk
  • : pbk

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Note

Bibliography: p. 233-234

Includes indexes

Some issues: Tokyo University international edition no. 173 (misprint?)

Description and Table of Contents

Volume

: hbk ISBN 9780691082639

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, ) attached to a cuspdidal automorphic representation of the group GL(2, /A), /A being the adele ring of the field, and L(s, ), whose definition is ultimately due to Hecke, is known to be entire. The main result, from which the existence of 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.
Volume

: pbk ISBN 9780691082721

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, ?) attached to a cuspdidal automorphic representation of the group GL(2, /A), /A being the adele ring of the field, and L(s, ?), whose definition is ultimately due to Hecke, is known to be entire. The main result, from which the existence of ? 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.

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