# Omega-theorems for the Riemann zeta function and its derivatives near the line $\mathrm{Re}\,s=1$

## TL;DR

This paper develops a generalized method to establish omega-theorems for the Riemann zeta function and its derivatives near the line Re s=1, advancing understanding of their growth behavior in that region.

## Contribution

It introduces a new generalized approach based on Zaitsev's method to prove omega-theorems for the zeta function and derivatives near Re s=1.

## Key findings

- Proves omega-theorems for the zeta function near Re s=1
- Establishes omega-theorems for derivatives of the zeta function
- Provides new bounds on the growth of zeta and its derivatives

## Abstract

We introduce a generalization of the method of S. P. Zaitsev. This generalization allows us to prove omega-theorems for the Riemann zeta function and its derivatives in some regions near the line $\mathrm{Re}\,s=1$.