The μ-invariant of anticyclotomic L-functions of imaginary quadratic fields

This paper considers the one-variable p-adic L-function which interpolates the L-values of anticyclotomic Hecke characters of an imaginary quadratic field K in which p splits. Fixing such a character with root number +1, the Iwasawa m-invariant of the associated branch of the p-adic L-function is computed as a sum of simple local contributions at the inert primes of K. The proof uses a result of Tonghai Yang to relate the p-adic L-function to a measure constructed out of the special values of theta functions with complex multiplication by K.