Central values of twisted base change $L$-functions associated to Hilbert modular forms

TL;DR

This paper employs the relative trace formula to establish non-vanishing and subconvexity results for twisted base change $L$-functions linked to Hilbert modular forms, especially those with supercuspidal local components, extending prior research.

Contribution

It introduces new non-vanishing and subconvexity results for twisted base change $L$-functions associated with Hilbert modular forms with supercuspidal local components, generalizing previous work.

Findings

Proves non-vanishing of certain $L$-functions.

Establishes subconvexity bounds for these $L$-functions.

Extends results to cases with supercuspidal local components.

Abstract

We use relative trace formula to prove a non-vanishing result and a subconvexity result for the twisted base change $L$-functions associated to Hilbert modular forms whose local components at ramified places are some supercuspidal representations. This generalizes the work of Feigon and Whitehouse.