Hardy-Ramanujan Journal |
In an earlier paper (Part VII, with the same title as the present paper) we proved results on the lower bound for the number of zeros of generalised Dirichlet series F(s)=∑∞n=1anλ−sn in regions of the type σ≥12−c/loglogT. In the present paper, the assumptions on the function F(s) are more restrictive but the conclusions about the zeros are stronger in two respects: the lower bound for σ can be taken closer to 12−C(loglogT)32(logT)−12 and the lower bound for the number of zeros is something like T/loglogT instead of the earlier bound >>T1−ε.