Number Theory Seminar

Title: On the first derivative of cyclotomic Katz p-adic L-functions at exceptional zeros.

Abstract: This talk is based on a joint work with Ming-Lun Hsieh studying the exceptional zeros conjecture of Katz p-adic L-functions. We will present a formula relating the first derivative of the cyclotomic Katz p-adic L-function attached to a ring class character of a general CM field to the product of an L-invariant and the value of some improved Katz p-adic L-function at s=0. In particular, we show that these Katz p-adic L-functions have a simple trivial zero if and only if their cyclotomic L-invariants are non-zero. Our method is based on congruence of Hilbert CM forms and Mazur's deformation theory