English

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}
}