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 contribution | Torsion behavior of epsilon factors of pairs |
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Original language | French |
Pages (from-to) | 1141 - 1173 |
Number of pages | 33 |
Journal | CANADIAN JOURNAL OF MATHEMATICS |
Volume | 53 |
Issue number | 6 |
Publication status | Published - 2001 |