# Niko Laaksonen: Prime Geodesic Theorem in the three-dimensional hyperbolic space

**Time: **
Wed 2018-12-19 11.00

**Lecturer: **
Niko Laaksonen

**Location: ** F11

The Prime Geodesic Theorem (PGT) states that the lengths of primitive

closed geodesics on a hyperbolic manifold have an asymptotic behaviour

analogous to the usual prime numbers. Through an explicit formula for

the Selberg zeta function we can relate the error term to certain

spectral exponential sums. In the past few years there has been a

renewed interest in this problem especially in two and three

dimensions. In this talk we will outline some recent progress on the

pointwise and second moment bounds of the error term in the PGT on

various three dimensional hyperbolic manifolds.