Kristian Holm

A Central Limit Theorem for Symplectic Lattice Point Counting Functions

We study a sequence of counting functions on the space of 2d-dimensional symplectic lattices where d is at least 4. Using a combinatorial device introduced by Björklund and Gorodnik in order to estimate cumulants (polynomial expressions in moments), we prove that our sequence satisfies a central limit theorem. The proof even involves obtaining new estimates on a certain height function introduced by Schmidt on the space of symplectic lattices.