Deformations of Theta Integrals and A Conjecture of Gross-Zagier
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2022
- DOI:
- 10.48550/arXiv.2204.10604
- arXiv:
- arXiv:2204.10604
- Bibcode:
- 2022arXiv220410604B
- Keywords:
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- Mathematics - Number Theory;
- 11F37;
- 11F41;
- 11G15
- E-Print:
- Improved exposition. Corrected typos and a missing factor of 2 in Theorem 5.1