Consider a group of measure preserving transformations acting on
a probability space. The limiting behavior of the nonconventional
ergodic averages associated with this action has been the subject
of much attention since the work of Furstenberg on...
A number is said to be $y$-smooth if all of its prime factors
are less than $y$. Such numbers appear in many places throughout
analytic and combinatorial number theory, and much work has been
done to investigate their distribution.
I will try to...
Thanks to the work of Katz and Sarnak on L-functions over
function fields, we know that the Frobenius classes associated to
L-functions of hyperelliptic curves over a finite field with $q$
elements, $F_{q}$, becomes equidistributed in the unitary...
We review the well known microscopic correspondence between
random zeros of the Riemann zeta-function and the eigenvalues of
random matrices, and discuss evidence that this correspondence
extends to larger mesoscopic collections of zeros or...
