Equidistribution of periodic points for modular correspondences (Q363204)

Assume that \(T\) is an exterior modular correspondence on an irreducible locally symmetric space \(X\) (the necessary definitions are too long to be reproduced here). In the present paper, the author shows that the isolated periodic points of order \(n\) of \(T\) are equidistributed (with respect to an appropriate measure) as \(n\) tends to infinity (Corollary 1.2). A second, more general result is also proved (Theorem 1.1). These results can also be applied (Theorem 3.1) in the context of the Arnold-Krylov-Guivarc'h theorem [\textit{V. I. Arnol'd} and \textit{A. L. Krylov}, Sov. Math., Dokl. 4, 1--5 (1963; Zbl 0237.34008); translation from Dokl. Akad. Nauk SSSR 148, 9--12 (1963)] and [\textit{Y. Guivarc'h}, C. R. Acad. Sci., Paris, Sér. A 268, 1020--1023 (1969; Zbl 0176.11703)].