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Abstract
In this paper, the analytic continuation formula of the Riemann zeta function is presented as a function of t2n, thus validating Riemann's claim that ε(t) allows itself to be developed in the power of t2. It is also shown that the root of ε(t) is always real. A theorem to validate the real roots is established.
References
On the number of Prime Number less than a given Quantity; Bernhard Riemann Translated by David R. Wilkins. Preliminary version: Dec. 1998 {Nonatsberichte der Berliner, Nov.1859}
An introduction to the theory of the Riemann zeta function, by S.J.Patterson.
On lower bounds for discriminants of algebraic number fields, M.Sc. thesis by S.A.Olorunsola (1980).
Complex variables and Application (Third edition) By Ruel V. Churchill, James W. Brown, and Roger F. Verhey.
Complex variables for scientists and engineers By John D. Paliouras.
Mathematical methods for physics and engineering; A comprehensive guide by K. F. Riley, M. P. Hobson and S. J. Bence.
Complex analysis (third edition) by Serge Lang; Department of mathematics Yale university New Haven, CT06520 USA. SPRINGER
Problem of the millennium; hypothesis.en.wikipedia.org/wiki/ Riemann-hypo.
Advanced Engineering mathematics By Erwin Kreyszig (8th Edition)
Supercomputers and the Riemann zeta function: A.M. Odlyzko; ATandT Bell Laboratories Murray Hcll, New jersey 07974
The Mathematical Unknown by John Derbyshire Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics; Joseph Henry Press, 412 pages, $24.95; Reviewer James Franklin
The Riemann hypothesis by Enrico Bombieri.
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