Resumen de Twisted Borcherds products on Hilbert modular surfaces and their CM values

Jan Hendrik Bruinier, Tonghai Yang

• We construct a family of rational functions on a Hilbert modular surface from the classical j-invariant and its Hecke translates. These functions are obtained by means of a multiplicative analogue of the Doi-Naganuma lifting and can be viewed as twisted Borcherds products. We then study when the value of at a CM point associated to a nonbiquadratic quartic CM field generates the ¿CM class field¿ of the reflex field. For the real quadratic field , we factorize the norm of some of these CM values to numerically.