ISSN: 2375-3927
International Journal of Mathematical Analysis and Applications  
Manuscript Information
 
 
Exact Proof of the Riemann Hypothesis
International Journal of Mathematical Analysis and Applications
Vol.3 , No. 2, Publication Date: Jul. 29, 2016, Page: 17-25
2012 Views Since July 29, 2016, 755 Downloads Since Jul. 29, 2016
 
 
Authors
 
[1]    

Fayez Fok Al Adeh, President: The Syrian Cosmological Society, Damascus, Syria.

 
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


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

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

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

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