Anticyclotomic exceptional zero phenomenon for Hilbert modular forms

TL;DR

This paper investigates the exceptional zero phenomenon for Hilbert modular forms in the anticyclotomic setting, deriving a formula that relates the leading term of p-adic L-functions to arithmetic L-invariants.

Contribution

It provides a new formula connecting the leading term of p-adic L-functions with arithmetic L-invariants in the anticyclotomic context for Hilbert modular forms.

Findings

Established a formula for the leading term of p-adic L-functions

Linked the exceptional zero phenomenon to arithmetic L-invariants

Extended understanding of p-adic L-functions in the anticyclotomic setting

Abstract

In this paper we study the exceptional zero phenomenon for Hilbert modular forms in the anticyclotomic setting. We prove a formula expressing the leading term of the p-adic L-functions via arithmetic L-invariants.