A class of approximations to the Riemann zeta function (Q2147833)

The paper under review is motivated by the work of \textit{Yu. V. Matiyasevich} on the fact that a few factors from the Euler product are sufficient for calculating the zeta function with high precision [Proc. Steklov Inst. Math. 299, 178--188 (2017; Zbl 1425.11193); translation in Tr. Mat. Inst. Steklova 299, 192--202 (2017)]. More precisely, the authors consider family of functions that approximate \(\zeta(s)\) with respect to a finite Euler product then answer to a number of conjectures raised in the above reference about their relationship with the Riemann zeta function.