Vol.3 , No. 2, Publication Date: Jul. 29, 2016, Page: 17-25
[1] | Fayez Fok Al Adeh, President: The Syrian Cosmological Society, Damascus, Syria. |
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
[01] | Titch marsh, E. C. (1999) “The Theory of the Riemann zeta –function”, London: Oxford University Press. |
[02] | Apostol, Tom M. (1974) “Mathematical Analysis”, Reading, Massachusetts; Addison –wesley Publishing Company. |
[03] | Edwards, H. M. (1974) “Riemann 's zeta function”, New York: Academic Press, Inc. |
[04] | Apostol, Tom M. (1976) “Introduction to Analytic Number Theory”, New York: Springer – Verlag. |
[05] | Koblits, Neal (1984) “P- adic Numbers, P – adic Analysis, and Zeta – Functions”, New York: Springer – Verlag. |
[06] | Geiner, Walter. Reinhardt, Joachim (1996)” Field Quantization”, Berlin: Springer – Verlag. |
[07] | Ribenboim, Paulo (1988) "The Book of Prime Number Records", Berlin: Springer – Verlag. |
[08] | Larson, Loren C. (1983) "Problem-Solving Through Problems", Berlin: Springer – Verlag. |
[09] | Wilf, Herbert S. (1994) "Generatingfunctionology", New York: Academic Press. |
[10] | Guy, Richard K. (1994) "Unsolved Problems in Number Theory", Berlin: Springer – Verlag. |