Number Theory Seminar
in Northeast Seoul

Markoff and Lagrange spectra for Hecke groups

Byungchul Cha  (Hongik University) 

March 20 (Fri)  2026, 10:30 ~ 11:30 

Asan science building 525

Abstract:  For an integer $q\ge 3$, \emph{the Hecke group $G_q$ of index $q$} is the subgroup generated by $z\mapsto -1/z$ and $z\mapsto z + 2\cos(\pi/q)$ of the orientation-preserving isometry group of the upper half plane. We study the structure of Markoff and Lagrange spectra of $G_q$. In particular, we characterize the initial discrete parts of these spectra. This mirrors classical results on the Markoff and Lagrange spectra of the real line. This is joint work with Dong Han Kim.