Eigenfunctions of transfer operators and cohomology
Number Theory
2008-11-25 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.0707.1203,
title = {Eigenfunctions of transfer operators and cohomology},
author = {R. W. Bruggeman and T. Muehlenbruch},
journal= {arXiv preprint arXiv:0707.1203},
year = {2008}
}