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)=n=1anλns 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.


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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