Torsion behavior of epsilon factors of pairs

Translated title of the contribution: Torsion behavior of epsilon factors of pairs

C J Bushnell, G Henniart

Research output: Contribution to journalArticlepeer-review

Abstract

Let F be a non-Archimedean local field, and psi a non-trivial additive character of F. Let n and n' be distinct positive integers. Let pi, pi' be irreducible supercuspidal representations of GL(n)(F), GL(n)' (F) respectively. We prove that there is c = c(pi, pi', psi) is an element of F-x such that for every tame quasicharacter chi of F-x we have epsilon(chi pi x pi', s, psi) = chi (c)(-1)epsilon(pi x pi', s, psi). We also treat some cases where n = n' and pi' = pi (boolean OR). These results are steps towards a proof of the Langlands conjecture for F, which would not use the geometry of modular-Shimura or Drinfeld-varieties.
Translated title of the contributionTorsion behavior of epsilon factors of pairs
Original languageFrench
Pages (from-to)1141 - 1173
Number of pages33
JournalCANADIAN JOURNAL OF MATHEMATICS
Volume53
Issue number6
Publication statusPublished - 2001

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