Vol. 260, No. 2, 2012

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On equality of arithmetic and analytic factors through local Langlands correspondence

Freydoon Shahidi

Vol. 260 (2012), No. 2, 695–715

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.

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
Received: 9 July 2012
Accepted: 4 September 2012
Published: 30 November 2012
Freydoon Shahidi
Department of Mathematics
Purdue University
West Lafayette, IN 47907
United States