Regularized theta lifts for orthogonal groups over totally real fields

Details Regularized theta lifts for orthogonal groups over totally real fields Regularized theta lifts for orthogonal groups over totally real fields

2009-08-21

arxiv.org/abs/0908.3076v3

Mathematics

Number Theory

43 pages, notation improved to match arXiv:1004.3720, references updated, minor corrections

Scientific paper

We define a regularized theta lift from SL_2 to orthogonal groups over totally real fields. It takes harmonic `Whittaker forms' to automorphic Green functions and weakly holomorphic Whittaker forms to meromorphic modular forms on orthogonal groups with zeros and poles supported on special divisors, generalizing Borcherds' work on automorphic products. To prove our results we use the spectral expansion of the lift and study its relationship with the cohomological theta lift of Kudla and Millson.

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