The derivative formula of p-adic L-functions for imaginary quadratic fields at trivial zeros
Journal
Annales Mathematiques du Quebec
Date Issued
2022
Author(s)
Abstract
The rank one Gross conjecture for Deligne–Ribet p-adic L-functions was solved in works of Darmon-Dasgupta-Pollack and Ventullo by the Eisenstein congruence among Hilbert modular forms. The purpose of this paper is to prove an analogue of the Gross conjecture for the Katz p-adic L-functions attached to imaginary quadratic fields via the congruences between CM forms and non-CM forms. The new ingredient is to apply the p-adic Rankin–Selberg method to construct a non-CM Hida family which is congruent to a Hida family of CM forms at the 1 + ε specialization. © 2022, Fondation Carl-Herz and Springer Nature Switzerland AG.
Subjects
L-functions; Modular forms; p-adic; Trivial zeros
Type
journal article