Montgomery-Rudnick-Sarnak theorem and k-tuple counting statistics in circular ensembles of random matrices.

Motivated by number theoretical results due to Montgomery, 
Hejhal, Rudnick, and Sarnak, we study limiting distribution of k-tuple 
smoothed counting statistics in circular ensembles of random matrices. 
Some of the results were obtained in  collaboration with Ander Aguirre 
and Josh Sumpter.