The Gross--Kohnen--Zagier theorem via p-adic uniformization

This article gives a new proof of the Gross--Kohnen--Zagier theorem for Shimura curves which exploits the p-adic uniformization of Cerednik--Drinfeld. The explicit description of CM points via this uniformization leads to an expression relating the Gross--Kohnen--Zagier generating series to the ordinary projection of the first derivative, with respect to a weight variable, of a p-adic family of positive definite ternary theta series.