## 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 = 1⁄2 + i, which is now known as the Riemann Hypothesis. Hence 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.

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### Submission history

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

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

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

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