On equality of arithmetic and analytic factors through local Langlands correspondence

Freydoon Shahidi

Vol. 260 (2012), No. 2, 695–715

DOI: 10.2140/pjm.2012.260.695

Abstract

In this article we pursue the problem of equality of Artin factors with those defined on the representation theoretic (analytic) side by the local Langlands correspondence. We propose a set of axioms for the factors on the analytic side which allows us to prove the equality of the factors. In the case of L-functions the equality can be proved in a number of cases appearing in the Langlands–Shahidi method since one of the axioms, stability under highly ramified twists, is already available for the L-functions coming from this method.

Keywords

Artin root numbers and L-functions, automorphic root numbers and L-functions, stability of root numbers

Mathematical Subject Classification 2010

Primary: 11F66, 11F70, 11F80

Secondary: 22E50

Milestones

Received: 9 July 2012

Accepted: 4 September 2012

Published: 30 November 2012