Conductors of twisted Weil--Deligne representations

Abstract

We study the behaviour of conductors of L-functions associated to certain Weil--Deligne representations under twisting. For each global field K we prove a sharp upper bound for the conductor of the Rankin--Selberg L-function associated to a pair of abelian varieties.

Major restructuring: strengthened main result on Rankin--Selberg L-functions and removed results on character twists. Comments welcome!