Twisted Borcherds products on Hilbert modular surfaces and their CM values

• Autores: Jan Hendrik Bruinier, Tonghai Yang
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 129, Nº 3, 2007, págs. 807-842
• Idioma: inglés
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• Resumen

  • 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.