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

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