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

Vendredi, 11. février 2022 - 14:00 - 15:00
Orateur: 

Adel Betina (Vienne) - à distance

Résumé: 

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.