Note on the Zeros of a Dirichlet Function

The existence of non trivial zeros off the critical line for a function obtained by analytic continuation of a particular Dirichlet series is studied. Our findings are in contradiction with some results of computations which were present in the field for a long time. In the first part of this note, we illustrate how the approximation errors may have had as effect inexact conclusions and in the second part we prove rigorously our point of view.