10.46298/hrj.1991.122
https://hrj.episciences.org/122
Balasubramanian, R
R
Balasubramanian
Ramachandra, K
K
Ramachandra
On the zeros of a class of generalised Dirichlet series-VIII
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 $>\!\!\!>T^{1-\varepsilon}$.
episciences.org
Borel-Carath\'eodory theorem
generalised Dirichlet series
[MATH] Mathematics [math]
2015-06-12
1991-01-01
1991-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01104792v1
2804-7370
https://hrj.episciences.org/122/pdf
VoR
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Hardy-Ramanujan Journal
Volume 14 - 1991
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