Twisted triple product p-adic L-functions and Hirzebruch-Zagier cycles

Let L/F be a quadratic extension of totally real number fields. For any prime unramified in L, we construct a p-adic L-function interpolating the central values of the twisted triple product L-functions attached to a p-nearly ordinary family of unitary cuspidal automorphic representations of GL_{2,L\times F}. Furthermore, when L is a real quadratic number field and p is a split prime, we prove a p-adic Gross-Zagier formula relating the values of the p-adic L-function outside the range of interpolation to the syntomic Abel-Jacobi image of generalized Hirzebruch-Zagier cycles.