How to prove the Riemann Hypothesis

  • Fayez Fok Al Adeh President of the Syrian Cosmological Society P.O.Box , 13187, Damascus, Syria
Keywords: Definite Integrel, Indefinite Integral, Variational Calculus.

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

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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,.

Published
2017-08-18
How to Cite
Al Adeh, F. (2017). How to prove the Riemann Hypothesis. Journal of Progressive Research in Mathematics, 12(2), 1853-1866. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1182
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