Deformations of Theta Integrals and A Conjecture of GrossZagier
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 DoiNaganuma theta lift of a deformed theta integral on hyperbolic space.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 DOI:
 10.48550/arXiv.2204.10604
 arXiv:
 arXiv:2204.10604
 Bibcode:
 2022arXiv220410604B
 Keywords:

 Mathematics  Number Theory;
 11F37;
 11F41;
 11G15
 EPrint:
 Improved exposition. Corrected typos and a missing factor of 2 in Theorem 5.1