Intersection numbers of Heegner divisors on Shimura curves (Q959029)

In several papers, Gross, Kohnen, and Zagier computed intersection numbers of certain Heegner divisors on integral models: There are two such formulas, where one uses two quadratic discriminants, while the other formula only makes use of one imaginary quadratic discriminant. In the present paper, the formula using two discriminants is generalized from the modular curves \(X_0(N)\) to certain Shimura curves defined over \(\mathbb Q\). One might remark that the multiplicities computed here, were already used by \textit{S. S. Kudla} [Ann. Math. (2) 146, No. 3, 545--646 (1997; Zbl 0990.11032)] to derive a relation between height pairings and special values of the derivatives of certain Eisenstein series.