The Gross--Kohnen--Zagier theorem via $p$-adic uniformization
Number Theory
2024-03-28 v1
Abstract
This article gives a new proof of the Gross--Kohnen--Zagier theorem for Shimura curves which exploits the -adic uniformization of Cerednik--Drinfeld. The explicit description of CM points via this uniformization leads to an expression relating the Gross--Kohnen--Zagier generating series to the ordinary projection of the first derivative, with respect to a weight variable, of a -adic family of positive definite ternary theta series.
Cite
@article{arxiv.2403.18688,
title = {The Gross--Kohnen--Zagier theorem via $p$-adic uniformization},
author = {Lea Beneish and Henri Darmon and Lennart Gehrmann and Martí Roset},
journal= {arXiv preprint arXiv:2403.18688},
year = {2024}
}