Deformations of Theta Integrals and A Conjecture of Gross-Zagier
Number Theory
2025-02-12 v3
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.
Keywords
Cite
@article{arxiv.2204.10604,
title = {Deformations of Theta Integrals and A Conjecture of Gross-Zagier},
author = {Jan H. Bruinier and Yingkun Li and Tonghai Yang},
journal= {arXiv preprint arXiv:2204.10604},
year = {2025}
}
Comments
Final version