Twisted Borcherds Products on Hilbert Modular Surfaces and Their Cm Values
نویسندگان
چکیده
We construct a natural family of rational functions Ψ̃m 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 Ψ̃m at a CM point associated to a non-biquadratic quartic CM field generates the ‘CM class field’ of the reflex field. For the real quadratic field Q( √ 5), we factorize the norm of some of these CM values to Q( √ 5) numerically.
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تاریخ انتشار 2005