# The limit of the Riemann zeta function and its nontrivial zeros

## TL;DR

This paper introduces a novel approach to explore the limit of the Riemann zeta function using Dirichlet's rearrangement theorem, aiming to shed light on its nontrivial zeros, which are central to number theory and the Riemann Hypothesis.

## Contribution

It presents the first exploration of the limit of the Riemann zeta function through a new rearrangement method, offering potential insights into its nontrivial zeros.

## Key findings

- Proposes a new method to analyze the zeta function limit
- Suggests a promising connection to nontrivial zeros
- Provides initial results for the limit of the zeta function

## Abstract

In this article, with a new approach, which is not discussed in the literature yet, the limit of the Riemann zeta function or Euler-Riemann zeta function is approximately explored by applying Dirichlet's rearrangement theorem for absolutely convergent series to the Riemann zeta function by rearranging its terms as geometric series for sufficiently large $n$. The limit of the Riemann zeta function or Euler-Riemann zeta functions, $\lim_{n\to\infty} \zeta(z)$, is first time explored. The limit obtained here is a very promising for the nontrivial or complex zeros of the Rieman zeta function.