Big Heegner points and special values of L-series

In Longo and Vigni (Manuscr Math 135:273–328, 2011), 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 Longo and Vigni (Manuscr Math 135:273–328, 2011) in the definite setting to certain higher weight analogues of the Bertolini–Darmon theta elements (Bertolini and Darmon in Invent Math 126:413–456, 1996). As a consequence of this relation, some of the conjectures in Longo and Vigni (Manuscr Math 135:273–328, 2011) are deduced from recent results of Chida and Hsieh (J Reine Angew Math, 2015).