Pollack, RobertKim, Chan-Ho2025-10-212025-10-212013https://hdl.handle.net/2144/515162013The main purpose of this dissertation is to examine how congruences between Hecke eigensystems of modular forms on the unit group of a definite quaternion algebra affect the Iwasawa invariants of their anticyclotomic p-adic L-functions. This work can be regarded as an application of Greenberg-Vatsal and Emerton-Pollack-Weston's ideas on the variation of Iwasawa invariants under congruences to the anticyclotomic setting. As an application, based on Pollack-Weston's generalization of Bertolini-Darmon's work, this work establishes infinitely many new examples of the anticyclotomic main conjecture for modular forms, which are not treated by Skinner-Urban's work. The idea comes from the philosophy of congruences developed by Vatsal, Greenberg-Vatsal, Greenberg, and Emerton-Pollack-Weston. We remark that our setting is more general than that of Skinner-Urban's work in two ways. First, the fixed prime p does not necessarily split in the imaginary quadratic field K. Second, our ramification condition on the residual Galois representations is weaker than Skinner-Urban's one. Note that the second condition allows us to deal with the case of positive mu-invariants.en-USMathematicsCongruencesIwasawa theoryModular formsp-adic L-functionsShimura curvesThesis/Dissertation2025-10-20