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arXiv · 2412.11130

Investigation about a statement equivalent to Riemann Hypothesis (RH)

Giovanni Lodone
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Abstract

First idea is to compute a quantity like the angular momentum with respect to (0, 0), of an unitary mass of coordinates (<[Xi(s)], =[Xi(s)]) while =[s] is the time, and, <[s] = constant. If we impose that the derivative along <[s], at points <[s] = 1/2 is grater than zero, then, we find exactly a known RH equivalence statement about relative maxima and minima of Xi(1/2 + i=[s]) along critical line. After representing this fictitious angular momentum by Euler Product, and, using PNT as a tool, it can be proved that this positivity condition is granted everywhere at least for Xi(1/2 + i=[s]) 6 = 0. So, if the above equivalence is true, it is found that off-critical line zeros must be excluded for Z(s) function along all critical strip . Further analysis on Euler Product(Lemma 2) has evidenced others shorter ways to same objective. Besides the converging spectrum of prime numbers is highlighted as a by-product.

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Giovanni Lodone. 2026-03-18. Investigation about a statement equivalent to Riemann Hypothesis (RH). https://arxiv.org/abs/2412.11130

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