• 1 Tata Institute for Fundamental Research

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 $\sigma$ can be taken closer to $\frac{1}{2}-C(\log\log T)(\log T)^{-1}$ and the lower bound for the number of zeros is like $T/\log\log\log T$.