On the mu-invariant of anticyclotomic p-adic L-functions for CM fields

TL;DR

This paper proves a conjecture regarding the mu-invariant of anticyclotomic p-adic L-functions for CM fields, providing an exact formula for self-dual characters and confirming the vanishing in certain cases.

Contribution

It establishes the vanishing of the mu-invariant for a broad class of p-adic L-functions and derives an explicit formula for self-dual branch characters, advancing understanding in Iwasawa theory.

Findings

Confirmed Gillard's conjecture on mu-invariant vanishing

Derived an explicit mu-invariant formula for self-dual characters

Extended results to anticyclotomic p-adic L-functions for CM fields

Abstract

In this article, we follow Hida's approach to study the mu-invariant of the anticyclotomic projection of p-adic Hecke L-functions for CM fields along a branch character. We prove a conjecture of Gillard on the vanishing of the mu-invariant and give an exact mu-invariant formula for self-dual branch characters.