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

R Balasubramanian (1) , K Ramachandra (1)

1 TIFR - Tata Institute for Fundamental Research

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 $\frac{1}{2}-C(\log\log T)(\log T)^{-1}$ and the lower bound for the number of zeros is like $T/\log\log\log T$.

Mots clés: generalised Dirichlet series; L-functions; Riemann zeta-function

Domaines: Mathématiques [math]

R Balasubramanian, K Ramachandra. On the zeros of a class of generalised Dirichlet series-IX. Hardy-Ramanujan Journal, 1991, Volume 14 - 1991, pp.34 - 43. ⟨10.46298/hrj.1991.123⟩. ⟨hal-01104799⟩