A Lyapunov exponent attached to modular functions

Paloma Bengoechea, Sebastián Herrero, Özlem Imamoglu

To each weakly holomorphic modular function $f\not\equiv 0$ for $\mathrm{SL}(2,\mathbb{Z})$, which is non-negative on the geodesic arc $\{e^{it}:\pi /3\le t\le 2\pi /3\}$, we attach…