Reversing Borcherds Lifts: A Survey

  • Bernhard HeimEmail author
  • Atsushi Murase
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 115)


This is a survey on our results towards the reversing of the multiplicative theta lift of Borcherds. First results on this topic had been obtained by Bruinier, proving that meromorphic automorphic forms F on the orthogonal group G = O(2, n + 2) with special divisor are Borcherds lifts. Holomorphic automorphic forms on G are Borcherds lifts if and only if they have a certain symmetry property. This leads to several applications. Special divisors (linear combinations of Heegner divisors) can be characterized by a symmetry property among all effective principal divisors. This gives a new proof and a generalization of parts of Bruinier’s result. We obtain recursion formulas for the Fourier-Jacobi coefficients of a Borcherds lift. Hence we have a direct link between Fourier-Jacobi coefficients and divisors.

Mathematics Subject Classification (2010)

11F11 11F50 11F55 11G18 



The authors thank the referee for sharpening the structure of the survey.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.German University of Technology in Oman,Halban CampusMuscatSultanate of Oman
  2. 2.Department of Mathematical Science,Faculty of ScienceKyoto Sangyo University Motoyama, KamigamoKita-kuJapan

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