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On convex co-compact hyperbolic surfaces , we investigate the behavior of nodal curves of real valued Eisenstein series , where  is the spectral parameter,  the direction at infinity. Eisenstein series are (non-) eigenfunctions of the Laplacian  satisfying . As  goes to infinity (the high energy limit), we show that, for generic , the number of intersections of nodal lines with any compact segment of geodesic grows like , up to multiplicative constants. Applications to the number of nodal domains inside the convex core of the surface are then derived.

On the Nodal Lines of Eisenstein Series on Schottky Surfaces