Non-zero values of a family of approximations of a class of $L$-functions

Arindam Roy, Kevin You

Consider the approximation ${\tilde{Z}}_N(s)={\sum }_{n=1}^N{n}^{-s}+\chi (s){\sum }_{n=1}^N{n}^{1-s}$ of the Riemann zeta function $\zeta (s)$, where $\chi (s)$ is the ratio of the gamma functions.…