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2020 $p$-adic distribution of CM points and Hecke orbits I: Convergence towards the Gauss point
Sebastián Herrero, Ricardo Menares, Juan Rivera-Letelier
Algebra Number Theory 14(5): 1239-1290 (2020). DOI: 10.2140/ant.2020.14.1239

Abstract

We study the asymptotic distribution of CM points on the moduli space of elliptic curves over p , as the discriminant of the underlying endomorphism ring varies. In contrast with the complex case, we show that there is no uniform distribution. In this paper we characterize all the sequences of discriminants for which the corresponding CM points converge towards the Gauss point of the Berkovich affine line. We also give an analogous characterization for Hecke orbits. In the companion paper we characterize all the remaining limit measures of CM points and Hecke orbits.

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Sebastián Herrero. Ricardo Menares. Juan Rivera-Letelier. "$p$-adic distribution of CM points and Hecke orbits I: Convergence towards the Gauss point." Algebra Number Theory 14 (5) 1239 - 1290, 2020. https://doi.org/10.2140/ant.2020.14.1239

Information

Received: 3 November 2018; Revised: 16 November 2019; Accepted: 6 February 2020; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07244794
MathSciNet: MR4129386
Digital Object Identifier: 10.2140/ant.2020.14.1239

Subjects:
Primary: 11G15
Secondary: 11F32 , 11S82

Keywords: Elliptic curves , equidistribution , Hecke correspondences

Rights: Copyright © 2020 Mathematical Sciences Publishers

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