Seminario / Andreatta
Mercoledì 17 aprile 2019 alle 16:00 in Aula Dottorato
il Prof. Fabrizio Andreatta
"Katz type $p$-adic $L$-functions for primes $p$ non-split in the CM field"
Abstract: 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.