In the papers [KW2, KW3] we introduced and studied a new type of the Selberg zeta function called by a higher Selberg zeta function. We have established the analytic properties, especially the functional equation of the higher Selberg zeta functions in [KW3]. Motivated by this study of higher Selberg zeta functions we formulate the problem for general zeta functions which have the Euler products and discuss their general features.
"Zeta extensions." Proc. Japan Acad. Ser. A Math. Sci. 78 (7) 126 - 130, Sept. 2002. https://doi.org/10.3792/pjaa.78.126