Orthogonal Eisenstein Series and Theta Lifts

Abstract

We show that the additive Borcherds lift of vector-valued non-holomorphic Eisenstein series are orthogonal non-holomorphic Eisenstein series for $O(2,l)$. Using this we give another proof that they have a meromorphic continuation, calculate their Fourier expansion and show that they have a functional equation analogous to the classical case. Moreover, we will investigate the image of Borcherds lift and give a sufficient condition for surjectivity.

26 pages

Cited by in corpus (1)

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