Asymptotic growth of the number of Reciprocal Classes in the Hecke Groups

Abstract

We estimate the asymptotic growth of reciprocal conjugacy classes in Hecke groups using their free product structure and word lengths of reciprocal elements. Our approach is different from other works in this direction and uses tools from basic probability theory.

14 pages. arXiv admin note: text overlap with arXiv:2411.00739