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 - 1991 - https://doi.org/10.46298/hrj.1991.122
On the zeros of a class of generalised Dirichlet series-VIIIArticle

Authors: R Balasubramanian 1; K Ramachandra 1

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

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