Poles of Eisenstein series on SL_n induced from maximal parabolics

Paul Feit

Vol. 155 (1992), No. 2, 229–250

DOI: 10.2140/pjm.1992.155.229

Abstract

The author locates poles for Eisenstein series on algebraic groups SL_n(Δ), where n ∈ ℕ and Δ is an arbitrary finite dimensional division algebra over a number field. An explicit family of non-holomorphic functions, which include series of arbitrary level, is characterized. Each series E(z,s) is induced from a character on a maximal parabolic. For each E(z,s) in the family, there is an explicit product Λ(s) of Γ-functions, L-functions and a polynomial term such that Λ(s)E(z,s) has only simple poles in the s variable.

Mathematical Subject Classification 2000

Primary: 11F30

Secondary: 11F55

Milestones

Received: 24 May 1990

Published: 1 October 1992