Juan Rivera-Letelier
University of Rochester
Title
Singular Moduli, p-adic Dynamics, and Hecke Orbits
Abstract
A singular modulus is the j-invariant of an elliptic curve with complex multiplication. These numbers play a central role in class field theory. We investigate their p-adic distribution on the Berkovich projective line, moving beyond the classical Archimedean setting. We describe how Hecke correspondences generate orbits of complex multiplication points and shape their distribution, explain why the Gauss point partially describes their limiting behavior, and how a p-adic Linnik-type equidistribution result completes the description. These dynamical insights lead to a concrete application to the arithmetic of singular moduli: There are at most finitely many of them that are S-units. The presentation highlights the interplay between number theory and p-adic dynamics.