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.
- ISBN10 0691082723
- ISBN13 9780691082721
- Publish Date 21 July 1980
- Publish Status Out of Print
- Out of Print 21 April 2017
- Publish Country US
- Imprint Princeton University Press
- Format Paperback (US Trade)
- Pages 248
- Language English
- URL https://press.princeton.edu/titles/574.html