2026/04/15 by Kâzım Büyükboduk, Peter Neamti
#math.NT
This paper provides a new proof of the p-adic Gross--Zagier formula for the p-adic L-function associated with the base change of a normalised cuspidal eigen-newform f of weight k ≥ 2 (and families of such) to an imaginary quadratic field K. Our results encompass both the classical p-ordinary cases and non-ordinary scenarios, including new cases where k > 2 and ordp(ap(f)) > 0. Unlike the traditional approach of comparing geometric and analytic kernels, we employ a ``wall-crossing'' strategy centred on the BDP formula and the theory of Beilinson--Flach elements.