The Iwasawa $\mu$-invariant of $p$-adic Hecke $L$-functions

Abstract

For an odd prime $p$, we compute the $\mu$-invariant of the anticyclotomic Katz $p$-adic $L$-function of a $p$-ordinary CM field if the conductor of the branch character is a product of primes split over the maximal real subfield. Except for rare cases where the root number of the $p$-adic functional equation is congruent to $-1$ modulo $p$, the invariant vanishes.