| viXra.org > General Mathematics > viXra:2101.0093 |
 |
 |
| viXra.org > General Mathematics > viXra:2101.0093 |
|
|
General Mathematics |
|
Authors: Nhat-Anh Phan
Redefining the set of all non null natural integers N∗ as the union of infinitely many disjoint sets, we prove the equiprobability for any integer of each said set to have either an odd or even number of prime factor(s) counted with multiplicity. The thus established equiprobability on N∗ allows us to use the standard normal distribution to establish that lim N→+∞ L(N)/√N=0, L(N) the summatory Liouville function. Recalling the Dirichlet series for the Liouville function we deduce that ζ(2s)/ζ(s), s = σ +it, is analytic for σ > 1/2, ζ(s) the Riemann zeta function. Consequently the veracity of the Riemann hypothesis is being established.
Comments: Copyright : All rights reserved. (Minor corrections on pages 3, 5, 14 and modifications on pages 4, 10, 15)
Download: PDF
[v1] 2021-01-14 23:33:49 (removed)
[v2] 2021-03-22 00:20:50 (removed)
[v3] 2021-04-05 22:21:02 (removed)
[v4] 2021-08-09 00:37:53
[v5] 2021-08-23 05:12:46
Unique-IP document downloads: 385 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.
| Third-Party Links: |
|