Improve Bounds of some Arithmetical Functions

Abstract

We show in this article the use of the norm function to get a new lower bound of Riemann-Zeta function  where.  This subject has been studied deeply by Hilberdink [HIL, 12]).  Getting a bound for the Riemann-Zeta function  in the critical strip is more challenging  for many reasons related to the behavior of the  Riemann-Zeta function in that strip. In the other words, the aim of this article  is to prove that  has a strict lower bound when the real part  is very closed to the line 1.  We state this in the  main theorem of this paper.