Stefano Beltraminelli, Danilo Merlini, Sergey Sekatskii
Published 2008-03-10Version 1
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.
Other representations of the Riemann Zeta function and an additional reformulation of the Riemann Hypothesis
Pair correlation of the zeros of the derivative of the Riemann $ΞΎ$-function
The zeros of the derivative of the Riemann zeta function near the critical line
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