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arXiv · 2606.19933

A note on equidistribution on a product of Shimura curves and Andr\'e--Oort

Francesco Maria Saettone
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Abstract

In this short note we show that Galois orbits of CM points equidistribute on a product of $r\ge 2$ non-isomorphic Shimura curves by applying the adelic toral-packet equidistribution theorem of Aka--Luethi--Michel--Wieser. As a consequence, we deduce Andr\'e--Oort for the product of those curves, previously studied by Edixhoven and Yafaev, replacing GRH by a Linnik-type splitting condition at two auxiliary primes.

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Francesco Maria Saettone. 2026-06-18. A note on equidistribution on a product of Shimura curves and Andr\'e--Oort. https://arxiv.org/abs/2606.19933

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