A Hidden Symmetry Related to the Riemann Hypothesis with the Primes into the Critical Strip

Details A Hidden Symmetry Related to the Riemann Hypothesis with the Primes into the Critical Strip A Hidden Symmetry Related to the Riemann Hypothesis with the Primes into the Critical Strip

2008-03-10

arxiv.org/abs/0803.1508v1

Mathematics

Number Theory

3 figures

Scientific paper

In this note concerning integrals involving the logarithm of the Riemann Zeta function, we extend some treatments given in previous pioneering works on the subject and introduce a more general set of Lorentz measures. We first obtain two new equivalent formulations of the Riemann Hypothesis (RH). Then with a special choice of the measure we formulate the RH as a ``hidden symmetry'', a global symmetry which connects the region outside the critical strip with that inside the critical strip. The Zeta function with all the primes appears as argument of the Zeta function in the critical strip. We then illustrate the treatment by a simple numerical experiment. The representation we obtain go a little more in the direction to believe that RH may eventually be true.

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