A note on equidistribution on a product of Shimura curves and André–Oort

Key Points

• This note aims to demonstrate the equidistribution of Galois orbits of CM points on Shimura curves.
• Applied the adelic toral-packet equidistribution theorem of Aka–Luethi–Michel–Wieser
• Analyzed the situation for products of non-isomorphic Shimura curves
• Replaced the Generalized Riemann Hypothesis with a Linnik-type splitting condition.
• Galois orbits of CM points were shown to equidistribute on products of Shimura curves.
• Established the André–Oort conjecture for those curves under relaxed conditions.