Symmetries of the transfer operator for ${\Gamma }_0(N)$ and a character deformation of the Selberg zeta function for ${\Gamma }_0(4)$

Markus Fraczek, Dieter Mayer

The transfer operator for ${\Gamma }_0(N)$ and trivial character ${\chi }_0$ possesses a finite group of symmetries generated by permutation matrices $P$ with $P^2=id$. Every such symmetry leads…