Photo by arthurbizkit from unsplash
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… Click to show full 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 $$s = 1$$ s = 1 whose residues yield holomorphic orthogonal modular forms that are Eisenstein series on the boundary. Moreover, we will investigate the image of this construction and give sufficient conditions for the surjectivity.
Journal Title: Mathematische Zeitschrift
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!