# Random Matrices and L-Functions 1.

## Nina Snaith

(Joint mini-series with Brian Conrey)
**Abstract: **
That a connection exists between random matrix theory and number theory has
been known ever since the 70s when H.L.Montgomery and F.J.Dyson discovered
over a cup of tea that the statistics of the zeros of the Riemann zeta
function calculated by the former agree with the eigenvalue distribution of
random matrices examined by the latter. This has led to random matrix
theory being applied in recent years to surprisingly diverse areas of
number theory, such as mean values of the Riemann zeta function and its
derivatives, ranks of elliptic curves and even to curious arithmetic
problems with seemingly no connection to random matrices at all. Random
matrix theory continues to surprise us with the depth and diversity of its
applications in number theory and we hope to demonstrate this by the
examples presented in the lecture.