The derivative formula of $p$-adic $L$-functions for imaginary quadratic fields at trivial zeros
Masataka Chida,
Ming-Lun Hsieh
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 fam… Show more
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