Equidistribution of periodic points for modular correspondences

TL;DR

This paper proves that isolated fixed points of powers of modular correspondences become evenly spread out over the space as the power increases, extending to general sequences of such correspondences.

Contribution

It establishes equidistribution results for fixed points of modular correspondences, including general sequences, which was not previously known.

Findings

Fixed points of T^n are equidistributed as n→∞

Results extend to general sequences of modular correspondences

Provides a measure-theoretic understanding of fixed point distribution

Abstract

Let T be an exterior modular correspondence on an irreducible locally symmetric space X. In this note, we show that the isolated fixed points of the power T^n are equidistributed with respect to the invariant measure on X as n tends to infinity. A similar statement is given for general sequences of modular correspondences.