Asymptotic properties of zeta functions

In this talk we will present the results concerning the asymptotic properties of zeta functions of global fields and varieties over them. We will discuss in more detail the explicit versions of the Brauer–Siegel type theorems and the results on the distribution of zeroes of $L$-functions of elliptic curves and modular forms. In the end we will present some open questions and further research directions in the asymptotic theory of zeta functions.