On the investigation of the Matsumoto zeta-function

Abstract

The study of the value distribution and the universality property of various zeta- and $L$-functions are one of interesting topics in analytic number theory. In this paper, we focus on the investigations of the polynomial Euler products or so called Matsumoto zeta-functions, and give an overview on results for this function.

Also, the facts from the personal and scientific life of Professor Kohji Matsumoto, who introduced this function, are given. It is impossible to describe briefly his all significant results, and we will focus only on the short overview of main directions of investigations.