4.4 Fabrizio Andreatta, Katz type p-adic L-functions for primes p non-split in the CM field, 11 June 2019, INdAM Program

INdAM Program on Serre Conjectures and the p-adic local Langlands program
I will discuss a way to construct anticyclotmic p-adic L-functions attached to an elliptic eigenform f and an imaginary quadratic field K, interpolating p-adically the central critical values of the Rankin L-functions of f twisted by anticyclotomic characters of higher infinity type. I will also provide p-adic Gross-Zagier formulae for these p-adic L-functions. Here the prime p is assumed to be inert or ramified in K. The case that p is split is due to Katz (for Eisenstein series) and Bertolini-Darmon-Prasana (for cuspidal eigenforms). This is joint work with Adrian Iovita.