3 problems

Let $\Gamma_0(N)$ be a congruence subgroup of Hecke type of level $N\ge 2$. For even $n\ge 2$, let $\wp_n(\Gamma_0(N))$ be the space of polynomial eigenfunctions of degree $n$ of t…

Let $\Gamma(N)$ be the principal congruence subgroup of $PSL(2,\mathbb Z)$ of level $N\ge 2$. For even $n\ge 2$, let $\wp_n(\Gamma(N))$ be the space of polynomial eigenfunctions of…

Let $L_s$ be the transfer operator for the geodesic flow associated with a modular group, and let the Lewis equation be the functional equation characterizing its polynomial eigenf…