Quotients of values of the Dedekind eta function (Q938253)

This paper investigates quotients \(\eta(A_j z)/\eta(A_{j-1} z)\) of the Dedekind eta function, where \(A_{j-1}\) and \(A_j\) are matrices whose rows are the coordinates of consecutive visible lattice points in a dilation \(X\Omega\) of a fixed region \(\Omega\) in \(\mathbb{R}^2\), and \(z\) is a fixed complex number in the upper half plane. In particular, the limiting distribution of these quotients is related to the index of Farey fractions introduced by \textit{R. R. Hall} and \textit{P. Shiu} [Mich. Math. J. 51, No. 1, 209--223 (2003; Zbl 1038.11062)].