How to prove the Riemann Hypothesis

Fayez Fok Al Adeh

Abstract


I have already discovered a simple proof of the Riemann Hypothesis. The hypothesis states
that the nontrivial zeros of the Riemann zeta function have real part equal to 0.5 . I assume
that any such zero is s =a+ bi .I use integral calculus in the first part of the proof. In the
second part I employ variational calculus. Through equations (50) to (59) I consider (a) as a
fixed exponent , and verify that a = 0.5 .From equation (60) onward I view (a) as a parameter
(a <0.5 ) and arrive at a contradiction. At the end of the proof (from equation (73)) and
through the assumption that (a) is a parameter, I verify again that a = 0.5


Keywords


Definite Integrel, Indefinite Integral, Variational Calculus.

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References


Titch marsh ,E.C.(1999)” The Theory of the Riemann zeta –function” ,London : Oxford University Press.

Apostol,Tom M.(1974)” Mathematical Analysis”, Reading ,Massachusetts ;Addison – wesley Publishing Company.

Edwards,H.M. (1974)” Riemann "s zeta function “, New York : Academic Press,Inc.

Apostol ,Tom M. (1976)” Introduction to Analytic Number Theory”, New York: Springer – Verlag,.

Koblits , Neal (1984)” P- adic Numbers , P – adic Analysis , and Zeta – Functions” ,New York : Springer – Verlag,.

Geiner ,Walter ; Reinhardt,Joachim (1996)” Field Quantization”,Berlin :Springer – Verlag,.


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