2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68845We 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 two. 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 study Faltings heights of arithmetic Hirzebruch-Zagier divisors.71 pages, Theorems 6.7 and 6.8 added, references updated, some typos removedNumber TheoryAlgebraic Geometry11F41, 14C17, 14G40, 14C20, 11G18text