On the value distribution of the Matsumoto zeta-function (Q812795)

\textit{K. Matsumoto} [Lect. Notes Math. 1434, 178--187 (1990; Zbl 0705.11050)] introduced a zeta function \(\phi(s)\), defined by an Euler product involving polynomials, that is a generalization of classical zeta-functions. The authors present a very clear and well-referenced account of the theory of the Matsumoto zeta-function and subsequent work, with particular emphasis on theorems concerning the frequency of the sets: \(\{\phi(\sigma+it)\in A\}\) or \(\{\phi(\sigma+it)\in A\}\) where \(A\) is a subset of \(\mathbb C\) or of the spaces of analytic or meromorphic functions, and where the imaginary part of the translations varies continuously in \([0,T]\). This paper is concerned with the discrete case, in which the frequency of the sets \(\{\phi(\sigma+ihm)\in A\}\) or \(\{\phi(\sigma+ihm)\in A \}\) is considered where the imaginary parts of the translations take values in some arithmetic progression and \(h>0\) is fixed.