March 27, 2024Open Access

The Gross--Kohnen--Zagier theorem via p-adic uniformization

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Abstract

This article gives a new proof of the Gross--Kohnen--Zagier theorem for Shimura curves which exploits the p-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 p-adic family of positive definite ternary theta series.

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Beneish et al. (Wed,) studied this question.

synapsesocial.com/papers/68e7230db6db64358769d44c https://doi.org/https://doi.org/10.48550/arxiv.2403.18688

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