p-adic equidistribution of modular geodesics and of Heegner points on Shimura curves

Patricio Pérez-Piña

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arXiv · 2405.16032

p-adic equidistribution of modular geodesics and of Heegner points on Shimura curves

Patricio Pérez-Piña

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Abstract

We propose a p-adic version of Duke's Theorem on the equidistribution of closed geodesics on modular curves. Our approach concerns quadratic fields split at p as well as a p-adic covering of the modular curve. We also prove an equidistribution result of Heegner points in the p-adic space attached to Shimura curves.

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Patricio Pérez-Piña. 2024-05-25. p-adic equidistribution of modular geodesics and of Heegner points on Shimura curves. https://arxiv.org/abs/2405.16032

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