Notes on the Riemann Zeta-Function

Abstract

In a recent paper [2] R. Balasubramanian and K. Ramachandra proved results like
max |ζ(1/2+it)|>t₀^-δ
where ∈ is an arbitrary positive constant, t₀ exceeds a positive constant depending on ∈ and C(∈) depends on ∈. In fact their results were very general and they could replace ζ(1/2+it) by F(σ+it) for very general Dirichlet series P(s), and prove (1) for F(σ+it). In this paper we record three theorems and indicate their proof. These are probably well-known to the experts in this field or at least within their easy reach. But the results are so interesting that they deserve to be printed.