TWISTED BORCHERDS PRODUCTS ON HILBERT MODULAR SURFACES AND THE REGULARIZED THETA LIFT

We construct a lifting from weakly holomorphic modular forms of weight 0 for SL2(ℤ) with integral Fourier coefficients to meromorphic Hilbert modular forms of weight 0 for the full Hilbert modular group of a real quadratic number field with an infinite product expansion and a divisor given by a linear combination of twisted Hirzebruch–Zagier divisors. The construction uses the singular theta lifting by considering a suitable twist of a Siegel theta function. We generalize the work by Bruinier and Yang who showed the existence of the lifting for prime discriminants using a different approach.