## Riemann’s Functional Equation is Not Valid and its Implication on the Riemann Hypothesis

**Authors:** Armando M. Evangelista Jr.

Riemann’s functional equation was formulated by Riemann that supposedly extended the domain of the Riemann zeta function from the right half-plane into the entire complex plane except at s = 1. It also led him to obtained a real function that contains zeros for some s. Now, the real function was also related to the zeta function which in turn has something to do with the distribution of prime numbers. This led him to obtained a formula for relating the zeros of the zeta function to the number of primes given a certain number. Riemann then conjectured that all the zeros of the zeta function are at s = ½ + ωi, which is now known as the Riemann Hypothesis. Hence the Riemann’s functional equation is the foundation upon which the Riemann Hypothesis is based. But the functional equation, as shall be shown here, is not valid such that the Riemann Hypothesis crumbles on its claim.

**Comments:** 10 Pages.

**Download:** **PDF**

### Submission history

[v1] 2018-08-28 11:37:38

[v2] 2018-10-26 06:33:56

[v3] 2018-11-13 17:31:31

[v4] 2019-04-24 10:03:19

**Unique-IP document downloads:** 114 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.*

*
*