Eigenfuncties of transfer operators and cohomology

R.W. Bruggeman; T. Mühlenbruch

doi:10.1016/j.jnt.2008.08.003

Eigenfuncties of transfer operators and cohomology

R.W. Bruggeman, T. Mühlenbruch

Afd Mathematisch Instituut

Fakultät Mathematik und Informatik

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The eigenfunctions with eigenvalues 1 or −1 of the transfer operator of Mayer are in bijective correspondence with the eigenfunctions with eigenvalue 1 of a transfer operator connected to the nearest integer continued fraction algorithm. This is shown by relating these eigenspaces of these operators to cohomology groups for the modular group with coefficients in certain principal series representations.

Original language	English
Pages (from-to)	158-181
Number of pages	24
Journal	Journal of Number Theory
Volume	129
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2008.08.003
Publication status	Published - 2009

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10.1016/j.jnt.2008.08.003

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title = "Eigenfuncties of transfer operators and cohomology",

abstract = "The eigenfunctions with eigenvalues 1 or −1 of the transfer operator of Mayer are in bijective correspondence with the eigenfunctions with eigenvalue 1 of a transfer operator connected to the nearest integer continued fraction algorithm. This is shown by relating these eigenspaces of these operators to cohomology groups for the modular group with coefficients in certain principal series representations.",

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AU - Mühlenbruch, T.

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AB - The eigenfunctions with eigenvalues 1 or −1 of the transfer operator of Mayer are in bijective correspondence with the eigenfunctions with eigenvalue 1 of a transfer operator connected to the nearest integer continued fraction algorithm. This is shown by relating these eigenspaces of these operators to cohomology groups for the modular group with coefficients in certain principal series representations.

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DO - 10.1016/j.jnt.2008.08.003

M3 - Article

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VL - 129

SP - 158

EP - 181

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

Eigenfuncties of transfer operators and cohomology

Abstract

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