On the theory of zeta-functions of root systems — Kohji Matsumoto (Nagoya University)

The theory of zeta-functions of root systems has been cultivated by the speaker with his colleagues Yasushi Komori and Hirofumi Tsumura. Recently (2023) we published a book, in which the main part of this theory is fully developed. The aim of the talk today is to describe the essence of this theory, mainly on the values at integer points, functional relations, analytic properties, and applications.