Equidistribution of Stark-Heegner and ATR cycles

TL;DR

This paper proves the equidistribution of certain S-arithmetic cycles related to RM and Stark-Heegner points, as well as Picard orbits of ATR cycles, advancing understanding of their distribution in number theory.

Contribution

It establishes the equidistribution of S-arithmetic cycles connected to RM and Stark-Heegner points and Picard orbits of ATR cycles, providing new insights into their distribution properties.

Findings

Proves equidistribution of S-arithmetic cycles related to RM and Stark-Heegner points.

Establishes equidistribution of Picard orbits of ATR cycles.

Advances understanding of the distribution of special cycles in arithmetic geometry.

Abstract

We prove the equidistribution of some cycles of S-arithmetic nature that are related to RM points and Stark-Heegner points. We also prove the equidistribution of Picard orbits of ATR cycles as defined by Darmon, Rotger and Zhao.