On the zeros of a class of generalised Dirichlet series. XIV (Q1322368)

[Parts XII and XIII have been reviewed in Zbl 0781.11033 and Zbl 0781.11034, respectively.] The main theorems in this paper give sufficient conditions for the existence of ``many'' zeros of a generalized Dirichlet series near the critical line \(\sigma=1/2\). The results are of the following general nature: If the series is ``sufficiently similar'' to the Riemann zeta- function in a certain sense, then the density of its zeros in neighbourhoods of the critical line is more or less comparable with that of the zeta-function.