Approximating the Riemann Zeta-function by Polynomials with Restricted Zeros

TL;DR

This paper explores polynomial approximations of the Riemann Zeta-function with constraints on zeros to better understand its properties and potential implications for number theory.

Contribution

It introduces methods for approximating the Zeta-function using polynomials with restricted zeros, a novel approach in analytic number theory.

Findings

Polynomials can approximate the Zeta-function with controlled zeros.

Restricted zero conditions influence the approximation accuracy.

Potential implications for the Riemann Hypothesis.

Abstract

We approximate the Riemann Zeta-Function by polynomials and Dirichlet polynomials with restricted zeros.