Geodesic
Deformations of Theta Integrals and A Conjecture of Gross-Zagier
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e54

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In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over a real quadratic field, which is constructed as the Doi-Naganuma theta lift of a deformed theta integral on hyperbolic 1-space. 
Bruinier, Jan H.; Li, Yingkun; Yang, Tonghai. Deformations of Theta Integrals and A Conjecture of Gross-Zagier. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e54. doi: 10.1017/fms.2024.139
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