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un théorème de finitude dans le spectre automorphe pour les formes intérieures de $\gl_{\lowercase{n}}$ sur un corps global

Published online by Cambridge University Press:  23 September 2005

alexandru ioan badulescu
alexandru ioan badulescu
Affiliation:
université de poitiers, département de mathématiques, téléport 2, boulevard marie et pierre curie, bp 30179, 86962 futuroscope chasseneuil cedex, francebadulesc@math.univ-poitiers.fr
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Abstract

a proof is given to show that for an inner form of $\gl_n$ over a global field of zero characteristic, there exist only a finite number of automorphic representations with fixed local factor (up to equivalence) at almost every place. what is new in comparison to earlier work (see a. i. badulescu and p. broussous, ‘un théorème de finitude’, compositio math. 132 (2002) 177–190) is the case when the local factors are not fixed at the infinite places, as well as the statement of the result for the automorphic spectrum, rather than the cuspidal one.

Keywords

11f70
Type
papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 5 , October 2005 , pp. 651 - 657
Copyright
the london mathematical society 2005

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