Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, Epiciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Journal articles

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

Abstract : 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 $>\!\!\!>T^{1-\varepsilon}$.
Document type :
Journal articles
Complete list of metadata

Cited literature [5 references]  Display  Hide  Download
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Thursday, January 22, 2015 - 9:24:10 AM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Thursday, April 23, 2015 - 10:07:01 AM


Explicit agreement for this submission




R Balasubramanian, K Ramachandra. On the zeros of a class of generalised Dirichlet series-VIII. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1991, Volume 14 - 1991, pp.21 - 33. ⟨10.46298/hrj.1991.122⟩. ⟨hal-01104792⟩



Record views


Files downloads