Featured Speaker :  Daniel Kriz

Title :   

Abstract : 

We will describe Katz's construction of a ppp-adic measure on the p∞p^{\infty}p∞ ray class group of CM fields, whose Mellin transform is a ppp-adic LLL-function interpolating critical values of Hecke LLL-functions. First, we will recall some basics of measures and the construction of the ppp-adic modular form-valued Eisenstein measure. Next, we will obtain Katz's measure by evaluating the Eisenstein measure at CM points. Finally, we will recover the aforementioned interpolation via Katz's insight that the values of the ppp-adic and complex differential operators at CM points coincide, which follows from the moduli-theoretic definitions of these operators.

algebraic geometrynumber theory