Chida MHsieh M.-L.MING-LUN HSIEH2022-11-112022-11-11202221954755https://www.scopus.com/inward/record.uri?eid=2-s2.0-85128365300&doi=10.1007%2fs40316-022-00198-6&partnerID=40&md5=deb9a264cfd4a3741a1c9d7708bc1aabhttps://scholars.lib.ntu.edu.tw/handle/123456789/624831The 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.L-functions; Modular forms; p-adic; Trivial zerosjournal article10.1007/s40316-022-00198-62-s2.0-85128365300