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arXiv · 2111.06245

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

Paul Kiefer
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Abstract

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.

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Paul Kiefer. 2021-11-11. Orthogonal Eisenstein Series at Harmonic Points and Modular Forms of Singular Weight. https://doi.org/10.1007/s00209-022-03011-w

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