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arXiv · 2204.10604

Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Jan H. Bruinier·Yingkun Li·Tonghai Yang
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Abstract

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 space.

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Jan H. Bruinier, Yingkun Li, Tonghai Yang. 2022-04-22. Deformations of Theta Integrals and A Conjecture of Gross-Zagier. https://arxiv.org/abs/2204.10604

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