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Twisted Borcherds products on Hilbert modular surfaces and their CM values
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 129, Number 3, June 2007
- pp. 807-841
- 10.1353/ajm.2007.0019
- Article
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Abstract
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.
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