Orthogonal Eisenstein Series at Harmonic Points and Modular Forms of Singular Weight

We investigate the behaviour of orthogonal non-holomorphic Eisenstein series at their harmonic points by using theta lifts. In the case of singular weight, we show that the orthogonal non-holomorphic Eisenstein series that can be written as a theta lift have a simple pole at $s=1$ whose residues yield holomorphic orthogonal modular forms that are Eisenstein series on the boundary and we give a sufficient condition on the surjectivity of this construction.