Rational period functions on \(G(\sqrt {2})\) and \(G(\sqrt {3})\) with hyperbolic poles are not Hecke eigenfunctions
type: Item
instance of: scholarly article
title: Rational period functions on \(G(\sqrt {2})\) and \(G(\sqrt {3})\) with hyperbolic poles are not Hecke eigenfunctions
zbMATH Open document ID: 0847.11018
author: Ellen Gethner
published in: Illinois Journal of Mathematics
publication date: 1996-05-14T00:00:00Z
review text: Using the existence of a linear map between the space of rational period functions defined on the Hecke group \(G(\sqrt p)\), \(p= 2\) or 3, and the space of rational period functions defined on the modular group it is established that a rational period function defined on \(G(\sqrt p)\) with a pole that is the fixed point of a hyperbolic element of \(G(\sqrt p)\) cannot be an eigenfunction of the induced Hecke operator. This extends the corresponding result for the modular group.
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F12
zbMATH DE Number: 878722
zbMATH Keywords: rational period functions
zbMATH Keywords: Hecke group
zbMATH Keywords: modular group
zbMATH Keywords: fixed point of a hyperbolic element
reviewed by: Gerhard Rosenberger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 878722