On the $\mu$-invariant of Katz $p$-adic $L$ functions attached to imaginary quadratic fields and applications

Abstract

We extend to $p=2$ and $p=3$ the result of Gillard and Schneps which says that the $\mu$-invariant of Katz $p$-adic $L$ functions attached to imaginary quadratic fields is zero for $p>3$. The arithmetic interpretation of this fact is given in the introduction.