In mathematics, Matsumoto zeta functions are a type of zeta function introduced by Kohji Matsumoto in 1990. They are functions of the form
ϕ ( s ) = ∏ p 1 A p ( p − s ) {\displaystyle \phi (s)=\prod _{p}{\frac {1}{A_{p}(p^{-s})}}}
where p is a prime and Ap is a polynomial.
References Matsumoto, Kohji (1990), "Value-distribution of zeta-functions", Analytic number theory ({T}okyo, 1988), Lecture Notes in Math., vol. 1434, Berlin, New York: Springer-Verlag, pp. 178–187, doi:10.1007/BFb0097134, ISBN 978-3-540-52787-9, MR 1071754