TY - JOUR
T1 - P-adic distribution of cm points and hecke orbits i
T2 - Convergence towards the gauss point
AU - Herrero, Sebastián
AU - Menares, Ricardo
AU - Rivera-Letelier, Juan
N1 - Publisher Copyright:
© 2020, Mathematical Sciences Publishers. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020
Y1 - 2020
N2 - We study the asymptotic distribution of CM points on the moduli space of elliptic curves over Cp, 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.
AB - We study the asymptotic distribution of CM points on the moduli space of elliptic curves over Cp, 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.
KW - Elliptic curves
KW - Equidistribution
KW - Hecke correspondences
UR - http://www.scopus.com/inward/record.url?scp=85090629372&partnerID=8YFLogxK
U2 - 10.2140/ant.2020.14.1239
DO - 10.2140/ant.2020.14.1239
M3 - Article
AN - SCOPUS:85090629372
SN - 1937-0652
VL - 14
SP - 1239
EP - 1290
JO - Algebra and Number Theory
JF - Algebra and Number Theory
IS - 5
ER -