A lower bound for the remainder in Weyl's law on negatively curved surfaces

Details A lower bound for the remainder in Weyl's law on negatively curved surfaces A lower bound for the remainder in Weyl's law on negatively curved surfaces

2006-12-10

arxiv.org/abs/math/0612250v3

Mathematics

Spectral Theory

27 pages; section 3 significantly revised. To appear in IMRN

Scientific paper

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.

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