This monograph treats one case of a series of conjectures by S.
Kudla, whose goal is to show that Fourier of Eisenstein series
encode information about the Arakelov intersection theory of
special cycles on Shimura varieties of orthogonal and unitary type.
Here, the Eisenstein series is a Hilbert modular form of weight one
over a real quadratic field, the Shimura variety is a classical
Hilbert modular surface, and the special cycles are complex
multiplication points and the Hirzebruch-Zagier divisors. By
developing new techniques in deformation theory, the authors
successfully compute the Arakelov intersection multiplicities of
these divisors, and show that they agree with the Fourier
coefficients of derivatives of Eisenstein series.
General
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