  We obtain an estimate from below for the remainder in Weyl's law on
negatively curved surfaces. In the constant curvature case, such a bound was
proved independently by Hejhal and Randol in 1976 using the Selberg zeta
function techniques. Our approach works in arbitrary negative curvature, and is
based on wave trace asymptotics for long times, equidistribution of closed
geodesics and small-scale microlocalization.
