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arXiv · 0707.1203

Eigenfunctions of transfer operators and cohomology

R. W. Bruggeman·T. Muehlenbruch
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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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R. W. Bruggeman, T. Muehlenbruch. 2007-07-09. Eigenfunctions of transfer operators and cohomology. https://doi.org/10.1016/j.jnt.2008.08.003

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