A generalization of S. Zhang’s local Gross-Zagier formula for GL(2) - Maurischat, Kathrin (Directions in Number Theory, 2016)
S. Zhang’s local Gross-Zagier formulae for GL2 can be interpreted as a fundamental lemma for some relative trace formulae. From this point of view we prove the existence of the corresponding local transfer. Further we construct universally defined geometric operators which realize the behavior of Hecke operators on the analytic side. We use them to give a proof of the local Gross-Zagier formula for GL2. We work locally and throughout computationally.