RETRACTED: The Proof of Riemann Hypothesis, the Key to the Door Is the Periodicity

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The author checked the published article in detail and found that the proof of "periodicity" is not strict. The author voluntarily withdraws the manuscript.

This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.
Editor guiding this retraction: Editorial Board of AM.
Please see the article page for more details. The full retraction notice in PDF is preceding the original paper which is marked "RETRACTED".

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The author declares no conflicts of interest regarding the publication of this paper.

References

[1] New Scientist (2018) Has the Riemann Hypothesis Been Solved?
https://www.newscientist.com/section/news/
[2] Titchmarsh, E.C. (1986) The Theory of the Riemann Zeta-Function. 2nd Edition, Edited and with a Preface by Heath-Brown, D.R., The Clarendon Press, Oxford University Press, Oxford.
[3] Edwards, H.M. (1974) Riemann’s Zeta Function. Academic Press, Waltham. (Reprinted by Dover Publications, Mineola, 2001).
[4] Borwein, P., Choi, S., Rooney, B. and Weirathmueller, A. (2007) The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike. Springer Press, New York.
https://doi.org/10.1007/978-0-387-72126-2
[5] Lu, C.H. (2016) Ramble on the Riemann Hypothesis. Tsinghua University Press, Beijing, 20-38. (In Chinese)
[6] Devlin, K.J. (2003) The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time. Basic Books, New York, 19-60.
[7] Riemann, B. (1998) On the Number of Prime Numbers Less than a Given Quantity. Translated by Wilkins, D.R.
http://www.claymath.org/library/historical/riemann/english/1.pdf
[8] Riemann, B. (2016) The Collected Works of Bernhard Riemann. Vol. 1, Chinese Edition, Translated by Li, P.L., Higher Education Press, Beijing, 127-135.
[9] Bombieri, E. (2000) Problems of the Millennium: The Riemann Hypothesis.
http://www.claymath.org/millennium-problems/riemann-hypothesis
[10] Lune, J., Riele, J.J. and Winter, D.T. (1986) On the Zeros of the Riemann Zeta Function in the Critical Strip, IV. Mathematics of Computation, 46, 667-681.
https://doi.org/10.1090/S0025-5718-1986-0829637-3
[11] Gourdon, X. (2004) The 1013 First Zeros of the Riemann Zeta Function, and Zeros Computation at Very Large Height.
http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeros1e13-1e24.pdf
[12] Stein, E.M. and Shakarchi, R. (2003) Princeton Lectures in Analysis I: Fourier Analysis, An Introduction. Princeton University Press, Princeton.
[13] Stein, E.M. and Shakarchi, R. (2003) Princeton Lectures in Analysis II: Complex Analysis. Princeton University Press, Princeton.
[14] Kudryavtseva, A.E., Saidak, F. and Zvengrowski, P. (2005) Riemann and His Zeta Function. Morfismos, 9, 1-48.
[15] Selberg, A. (1942) On the Zeros of the Zeta-Function of Riemann. Norske Vid. Selsk. Forh. Trondhjem, 15, 59-62.
[16] Levinson, N. (1974) More than One-Third of the Zeros of the Riemann Zeta-Function Are on σ =1/2. Advances in Mathematics, 13, 383-436.
https://doi.org/10.1016/0001-8708(74)90074-7
[17] Conrey, J.B. (1989) More than Two Fifths of the Zeros of the Riemann Zeta Function Are On the Critical Line. Journal für die reine und angewandte Mathematik, No. 399, 1-26.
https://doi.org/10.1515/crll.1989.399.1
[18] Odlyzko, A. (n.d.) Tables of Zeros of the Riemann Zeta Function.
http://www.dtc.umn.edu/~odlyzko/zeta_tables/index.html
[19] Gilbarg, D. and Trudinger, N.S. (2001) Laplace’s Equation. In: Elliptic Partial Differential Equations of Second Order, Vol. 224, Springer-Verlag, Berlin, Heidelberg, 13-30.
https://doi.org/10.1007/978-3-642-61798-0_2
[20] Odlyzko, A.M. (1989) Supercomputers and the Riemann Zeta Function, Supercomputing 89: Supercomputing Structures & Computations. Proceedings of 4th International Conference on Supercomputing, International Supercomputing Institute, 348-352.
[21] Wang, J.L. (2018) Fast Algorithm for the Travelling Salesman Problem and the Proof of P = NP. Applied Mathematics, 9, 1351-1359.
https://doi.org/10.4236/am.2018.912088

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