Reviewed by Rainer Schulze-Pillot References

Abstract

Twisted Borcherds products on Hilbert modular surfaces and the regularized theta lift. (English summary) Int. J. Number Theory 6 (2010), no. 7, 1473–1489.1793-7310 The article generalizes work of J. H. Bruinier and T. H. Yang [Amer. J. Math. 129 (2007), no. 3, 807–841; MR2325105 (2008f:11057)] which constructed a Borcherds-type lift from weakly holomorphic modular forms of weight zero for the full modular group SL2(Z) to Hilbert modular forms of weight zero for the full Hilbert modular group of a real quadratic number field of prime discriminant. The restriction to prime discriminants is removed here. This is made possible by changing the method of proof, using (as already suggested in the article of Bruinier and Yang) a regularized theta lifting instead of Green functions and Poincaré series. Most of the work goes into the proof of the transformation properties of the twisted Siegel theta function employed in th

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