On anticyclotomic <i>μ</i>-invariants of modular forms

Abstract

Abstract We prove the μ -part of the main conjecture for modular forms along the anticyclotomic Z p -extension of a quadratic imaginary field. Our proof consists of first giving an explicit formula for the algebraic μ -invariant, and then using results of Ribet and Takahashi showing that our formula agrees with Vatsal’s formula for the analytic μ -invariant.