Interesting connections have been discovered between the statistics of
eigenvalues of groups of random matrices and the statistics of
zeros of families of L-functions from number theory.
These connections have been pushed further
to relate the moments and the value distribution of characteristic
polynomials from random matrix theory with the moments and the value
distribution of families of L-functions.
The purpose of these lectures will be to illustrate these phenomena.
Some of the topics covered will be:
the basic properties of the Riemann zeta-function
an introduction to some families of L-functions
some statistics from random matrix theory
Katz - Sarnak work on zeros of zeta functions over finite fields
theory and numerics about the distributions of zeros of L-functions
