Number Theory Seminar

The Gross-Kohnen-Zagier theorem says that certain generating series of CM points are modular forms of weight 3/2 in the Jacobian of the modular curve $X_0(N)$. In this talk, I will discuss a new proof of the Gross--Kohnen--Zagier formula for Shimura curves which uses the $p$-adic uniformisation of Cerednik--Drinfeld. The explicit description of CM points via this uniformisation leads to an expression for the Gross--Kohnen--Zagier generating series as the ordinary projection of the first derivative of a $p$-adic family of positive definite ternary theta series. This is joint work with Henri Darmon, Lennart Gehrmann and Marti Roset Julia.