Although Riemann’s zeta function is complex imaginary the original zeta function is simplex real (see http://www.maa.org/devlin/Zeta.PDF). It was discovered at the Berlin Academy by Leonhard Euler (1707-1783) in 1748 at the height of his mathematical productivity where and when he just left St Petersburg Academy in 1741 of 25 years of research concerning the infinite series expansions of real and complex variables of analytic or holomorphic functions. A function is analytic at a point if there is a neighborhood N of this point such that the function is differentiable at every point of N. An alternate and equivalent definition is that if the neighborhood’s Taylor’s infinite series expansions exist. A function is also analytic in a region if it is analytic at every point of that region. The existence of differentiability implies the infinitesimal connection between continuity and quantized divisibility. These combined properties of simultaneous continuity and divisibility defined all prime numbers as the atoms or modular forms of the space-time continuum. These modular forms are describable by distinct Hadamard matrices of H-pluses and H-minuses of any arbitrary order and dimension. However, modular forms imply that all infinite series expansions of analytic functions must be convergent that is to say that the infinite sum has a limit. Unfortunately, Euler was able to prove only for the case where the reciprocal power of the real zeta function is an even number, specifically, the even number 2. The limit was found to be p²/6. The logical implication for squares of energy is unavoidable. On the other hand, the Riemann’s zeta function has its reciprocal powers equal to a real complex imaginary number x+iy. See http://mathworld.wolfram.com/RiemannZetaFunction.html and the fact that the zeta function is equated to zero imply that its limit exists and is zero without the provision of a proof. Moreover for x=1/2 all the roots of the zeta function lie on a straight line. The boldness of Riemann’s hypothesis depends on two factors: the existence of a zero limit and the conjecture that all these zeros lie on a straight line.


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