## R Balasubramanian ; K Ramachandra - On the zeros of a class of generalised Dirichlet series-VIII

hrj:122 - Hardy-Ramanujan Journal, January 1, 1991, Volume 14 - https://doi.org/10.46298/hrj.1991.122
On the zeros of a class of generalised Dirichlet series-VIII

Authors: 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 $F(s)= \sum_{n=1}^{\infty} a_n\lambda^{-s}_n$ in regions of the type $\sigma\geq\frac{1}{2}-c/\log\log T$. 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 $\frac{1}{2}-C(\log\log T)^{\frac{3}{2}}(\log T)^{-\frac{1}{2}}$ and the lower bound for the number of zeros is something like $T/\log\log T$ instead of the earlier bound $>\!\!\!>T^{1-\varepsilon}$.

Volume: Volume 14
Published on: January 1, 1991
Submitted on: March 3, 2015
Keywords: Borel-Carath\'eodory theorem,generalised Dirichlet series,[MATH] Mathematics [math]

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