### The values of the Dedekind-Rademacher cocycle at RM multiplication points

Heilbronn Number Theory Seminar

11th December 2019, 11:00 am – 12:00 pm

Fry Building, 2.04

A rigid meromorphic cocycle is a class in the first cohomology of the group SL2(Z[1/p]) acting on the non-zero rigid meromorphic functions on the Drinfeld p-adic upper half plane by Mobius transformation. Rigid meromorphic cocycles can be evaluated at points of real multiplication, and their RM values conjecturally lie in the ring class field of real quadratic fields, suggesting striking analogies with the classical theory of complex multiplication.

In this talk, we study derivatives of a p-adic family of Hilbert Eisenstein series, in analogy to the work of Gross and Zagier. We relate its diagonal restriction to certain RM values of rigid meromorphic cocycles. As an application, we prove that the RM values of the Dedekind-Rademacher cocycle are algebraic. This is joint work with Henri Darmon and Jan Vonk.

## Comments are closed.