On zeros of Riemann's zeta function in the negative half of the complex plane. Dirichlet lines and the concept of Riemann lines


Academic Paper, 2022

16 Pages, Grade: 2.0


Abstract or Introduction

The concept of a Dirichlet line in the complex plane was developed in [1]. This analysis is here extended to define another line in the complex plane, called by the author, a Riemann line. These lines are shown to extend throughout the whole of the complex plane. Along Dirichlet lines the zeta function is given by the negative of Dirichlet's alternating function for a real number, whilst along a Riemann line the zeta function is given by the zeta function for a real number. It is shown that there are an infinite number of these lines in the complex plane and, at the intersection of which with an ordinate line passing through any of the trivial zeros of the Riemann zeta function a zero of a Riemann zeta function is located.
A distinguishing characteristic of the Dirichlet lines and the Riemann lines is that they are associated with a multiplier which is an odd number for a Dirichlet line and an evev number for a Riemann line.

Details

Title
On zeros of Riemann's zeta function in the negative half of the complex plane. Dirichlet lines and the concept of Riemann lines
Grade
2.0
Author
Year
2022
Pages
16
Catalog Number
V1240198
Language
English
Tags
riemann, dirichlet
Quote paper
William Fidler (Author), 2022, On zeros of Riemann's zeta function in the negative half of the complex plane. Dirichlet lines and the concept of Riemann lines, Munich, GRIN Verlag, https://www.grin.com/document/1240198

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