Zeta statistics

Abstract: In this talk, we will introduce several different topologies in which a sequence of zeta functions of varieties over a finite field can be taken to converge. These topologies will be defined in terms of the sizes of the coefficients of the power series expansions at zero or in terms of the zeros and poles. We will explain how these types of convergence can be interpreted arithmetically and/or geometrically, and how this leads to a conjectural way of unifying arithmetic and motivic statistics. As evidence for our conjectures we will mention some convergence results for spaces of zero-cycles. This is joint work with Ronno Das and Sean Howe.

number theory

Audience: researchers in the topic

Around Frobenius distributions and related topics II