Giovanni Prodi Visiting Professor Winter Term 2017/2018
Prof. Dr. Roma Kačinskaitė works at the University Šiauliai and the Vytautas Magnus University in Kaunas (both in Lithuania). Her research considers questions around the analytic properties of so-called Dirichlet series and Euler products, rersp. their analytic continuations. Those series and products are generating functions built from arithmetical data (as, for example, prime numbers or residue class characters).
The most famous example is the Riemann zeta-function; its distribution of zeros is an open millennium problem. Using probabilistic methods, Prof. Kačinskaitė attempts to prove limit theorems in order to learn about the value-distribution of this or other zeta- and L-functions. One of the most remarkable applications of these methods is Voronin's universality theorem that, roughly speaking, every non-vanishing analytic function, defined on a small disk, can be approximated as good as we please by certain translates of the Riemann zeta-function. That means a single function allows to approximate a large class of functions!
These topics will be treated in Prof. Kačinskaitė's lectures (in English, in the Master programme): "Analytic
Number Theory"'' has a focus on classical questions concerning the distribution of prime numbers by use of analytic methods
and "Universality for Zeta-Functions" deals with the above mentioned universality phenomenon.