Big Heegner points and special values of $L$-series

Abstract: In \cite{LV}, Howard's construction of big Heegner points on modular curves was extended to general Shimura curves over the rationals. In this paper, we relate the higher weight specializations of the big Heegner points of \emph{loc.cit.} in the definite setting to certain higher weight analogues of the Bertolini-Darmon theta elements. As a consequence of this relation, some of the conjectures formulated in \cite{LV} are deduced from recent results of Chida-Hsieh.