Heegner Divisors and Nonholomorphic Modular Forms

By Jens Funke. Compositio Mathematica, 2002

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Cycle integrals of the j-function and mock modular forms (2011, methodology): “(See [16], [5] for the use of regularized theta lifts in the negative discriminants case.”
Regularized theta liftings and periods of modular functions (2011, methodology): “Applying ξ1/2 to Hh(τ, f) we recover the generating series for the traces of modular functions over CM points obtained in [5] (and [11] for f = 1) which in turn generalized the results of Zagier [28, 29].”
On two geometric theta lifts (2002, background): “s Z(h,n) are a collection of points in this situation. Hence ΛKM is deﬁned on H0(X) ≃ R and for q≥ 3, the lift Λ(τ,η) is a holomorphic modular form ([FM1]), while for q= 2, it is non-holomorphic, see [Fu]. 5.2. The(Generalized) BorcherdsLift. 5.2.1. The Hermitian Case. Here we assume that V has sign”