a1 Department of Mathematics, University of Vermont, Burlington, VT 05405, U.S.A.
a2 Department of Mathematics, Concordia University, Montréal, H3G 1M8, Canada
Let E/F be a finite normal extension of number fields with Galois group G. For each virtual character χ of G, denote by L(s, χ) = L(s, χ, F) the Artin L-series attached to χ. It is defined for Re (s) > 1 by an Euler product which is absolutely convergent, making it holomorphic in this half plane. Artin's holomorphy conjecture asserts that, if χ is a character, L(s, χ) has a continuation to the entire s-plane, analytic except possibly for-a pole at s = 1 of multiplicity equal to χ, 1, where 1 denotes the trivial character. A well-known group-theoretic result of Brauer implies that L(s, χ) has a meromorphic continuation for all s.
(Received November 24 1987)
(Revised June 14 1988)
p1 Current address: Department of Mathematics, University of Toronto, Toronto, Canada, M5S 1A1.