Eigenfunctions of transfer operators and cohomology

Details Eigenfunctions of transfer operators and cohomology Eigenfunctions of transfer operators and cohomology

2007-07-09

arxiv.org/abs/0707.1203v1

Journal of Number Theory 129 (2009) 158-181

Mathematics

Number Theory

Scientific paper

10.1016/j.jnt.2008.08.003

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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