Abstract
We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight . Moreover, we determine the arithmetic self-intersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors
Citation
Jan H. Bruinier. José I. Burgos Gil. Ulf Kühn. "Borcherds products and arithmetic intersection theory on Hilbert modular surfaces." Duke Math. J. 139 (1) 1 - 88, 15 July 2007. https://doi.org/10.1215/S0012-7094-07-13911-5
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