Conductors of twisted Weil--Deligne representations

TL;DR

This paper investigates how conductors of L-functions linked to Weil--Deligne representations change when twisted, providing bounds for conductors of Rankin--Selberg L-functions of abelian varieties over global fields.

Contribution

It establishes a sharp upper bound for the conductor of Rankin--Selberg L-functions of abelian varieties over global fields, advancing understanding of their behavior under twisting.

Findings

Proved a sharp upper bound for conductors of Rankin--Selberg L-functions.

Analyzed the behavior of conductors under twisting of Weil--Deligne representations.

Enhanced understanding of L-function conductors in the context of abelian varieties.

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.