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

2024/03/27 by Lea Beneish, Henri Darmon, Beneish, Lea +5
Mathematics · #advanced mathematical theories #Meromorphic and Entire Functions #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2403.18688

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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