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Twists of a General Class of $L$-Functions by Highly Ramified Characters

Published:2000-09-01
Printed: Sep 2000
• Freydoon Shahidi
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Abstract

It is shown that given a local $L$-function defined by Langlands-Shahidi method, there exists a highly ramified character of the group which when is twisted with the original representation leads to a trivial $L$-function.
 MSC Classifications: 11F70 - Representation-theoretic methods; automorphic representations over local and global fields 22E35 - Analysis on $p$-adic Lie groups 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]