Growth and nodal current of complexified horocycle eigenfunctions

Mikhail Dubashinskiy

We study horocycle eigenfunctions at Lobachevsky plane. They are functions $u:\mathbb{H}={\mathbb{C}}^{+}=\{z\in \mathbb{C}:\Im z>0\}\to \mathbb{C}$ such that $\left(-y^2\left(\f…