Volume 14 - 1991


1. Proof of some conjectures on the mean-value of Titchmarsh series-II

R Balasubramanian ; K Ramachandra.
In this paper, we give lower bounds for H0|F(it)|kdt, where k=1 or 2 and F(s) is a Dirichlet series of a certain kind. Since the conditions on F(s) are relaxed, the bounds are somewhat smaller than those obtained previously.

2. On the zeros of a class of generalised Dirichlet series-VIII

R Balasubramanian ; K Ramachandra.
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=1anλsn in regions of the type σ12c/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 12C(loglogT)32(logT)12 and the lower bound for the number of zeros is something like T/loglogT instead of the earlier bound >>T1ε.

3. On the zeros of a class of generalised Dirichlet series-IX

R Balasubramanian ; K Ramachandra.
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 12C(loglogT)(logT)1 and the lower bound for the number of zeros is like T/logloglogT.