Number Theory Seminar

The classical theory of complex multiplication implies that the value of the modular j-function at a CM point is an algebraic number. In the 1980's, Gross and Zagier conjectured that similar phenomena also happen for the resolvent kernel at integral spectral parameters, which are called higher Green functions. In this talk, we will look at its generalization to the case of orthogonal Shimura varieties, and recent results that resolve some of these conjectures.