In 2018 Keating, Rodgers, Roditty-Gershon and Rudnick studied the mean-square of sums of the divisor function dk(f) over short intervals and over arithmetic progressions for the function field 𝔽q[T]. By results from the Katz and Sarnak philosophy, they were able to relate these problems to certain integrals over the ensemble of unitary matrices when q goes to infinity. We study similar problems leading to integrals over the ensembles of symplectic and orthogonal matrices when q goes to infinity.
This is joint work with Vivian Kuperberg.
This video is part of the Number Theory Web Seminar series.
