Authors: John Yuk Ching Ting
The triple countable infinite sets of (i) x-axis intercepts, (ii) y-axis intercepts, and (iii) both x- and y-axes [formally known as the 'Origin'] intercepts in Riemann zeta function are intimately related to each other simply because they all constitute complementary points of intersection arising from the single [exact same] countable infinite set of curves generated by this function. This [complete] relationship amongst all three sets of intercepts will enable us to simultaneously study important intrinsic properties derived from all those intercepts in a mathematically consistent manner which then provides the rigorous proof for Riemann hypothesis as well as fully explain x-axis intercepts (which is the usual traditionally-dubbed 'Gram points') and y-axis intercepts. Riemann hypothesis involves analysis of all nontrivial zeros of Riemann zeta function and refers to the celebrated proposal by famous German mathematician Bernhard Riemann in 1859 whereby all nontrivial zeros are conjectured to be located on the critical line [or equivalently stated as all nontrivial zeros are conjectured to exactly match the Origin intercepts]. Concepts from the Hybrid method of Integer Sequence classification, together with our key formulae coined Sigma-Power Laws, are some of the important mathematical tools employed in this paper to successfully achieve our proof. Not least in [again] using the same 'Virtual container' method in this current research paper, there are other additional deeply inseparable mathematical connections between the content of this paper and our 2017-dated publication on the dual source of prime number infiniteness entitled "Rigorous proofs for Polignac's and Twin prime conjectures using Information-Complexity conservation" http://viXra.org/abs/1703.0115.
Comments: 20 Pages. This research paper contains the rigorous proof for Riemann hypothesis.
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