Series expansions for Maass forms on the full modular group from the Farey transfer operators

Claudio Bonanno, Stefano Isola

Published 2016-07-08Version 1

We analyze the relations previously established by Mayer, Lewis-Zagier and the authors, among the eigenfunctions of the transfer operators of the Gauss and the Farey maps, the solutions of the Lewis-Zagier three-term functional equation and the Maass forms on the modular surface $SL(2,\Z)\backslash \HH$. As main result, we establish new series expansions for the Maass cusp forms and the non-holomorphic Eisenstein series restricted to the imaginary axis.