Quotients of values of the Dedekind eta function
type: Item
instance of: scholarly article
title: Quotients of values of the Dedekind eta function
zbMATH Open document ID: 1144.11034
author: Emre Alkan
author: Maosheng Xiong
author: Alexandru Zaharescu
published in: Mathematische Annalen
publication date: 2008-08-18T00:00:00Z
review text: 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)].
reviewed by: Tom M. Apostol
Mathematics Subject Classification ID: 11F20
zbMATH DE Number: 5313065
MaRDI profile type: Publication
full work available at URL: s00208-008-0228-1
OpenAlex ID: W2077263091
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DOI: 10.1007/S00208-008-0228-1
description: scientific article; zbMATH DE number 5313065