Fourier decay, Green's kernel and Schottky groups

Abstract: In this note, I would like to discuss an approach to the construction of Green's function on algebraic surfaces, indicated by Manin, towards the computation of the Green's function on surfaces using Schottky uniformization. We shall see that the exact geometric interpretation of the formula mentioned there is obscure, and try to remedy the situation by investigating convergence of deformations of that formula.