On the Riemann Hypothesis


Academic Paper, 2021

13 Pages, Grade: 2.00


Abstract or Introduction

It is demonstrated in this work that we may construct an infinite number of strips in the complex plane having the same 'dimensions as the Critical Strip and which are devoid of Riemann zeros except on the line of symmetry. It is shown that the number of zeros on each line is infinite, indeed, there is a Riemann zero at infinity.

It is posited that a form of the Riemann conjecture is verified in each strip. It is shown that each integer in the infinite set of the integers has an associated Riemann zero and that the imaginary parts of the complex number at which the zeros are located are proportional to the 'local' asymptote to the prime counting function. A connection between the prime counting function and the zeta function is established. A limited distribution of the Riemann zeros corresponding to their respective prime numbers is constructed and it is seen that, at least over this range, the two are correlated, albeit non-linearly.

It is demonstrated that the imaginary part of the complex number locating a Riemann zero may, for any integer that can be articulated, be obtained by a few keystrokes of a hand calculator.

Details

Title
On the Riemann Hypothesis
Grade
2.00
Author
Year
2021
Pages
13
Catalog Number
V993094
ISBN (eBook)
9783346388575
ISBN (Book)
9783346388582
Language
English
Tags
riemann, hypothesis
Quote paper
William Fidler (Author), 2021, On the Riemann Hypothesis, Munich, GRIN Verlag, https://www.grin.com/document/993094

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