This theorem solves in a way simple and elegant the following original problem of Gallo: “It ‘s possible to represent complex non-trivial zeros of the Riemann zeta function on the real axis in terms of symmetry and how?” This problem was solved by the Italian mathematician Onofrio Gallo (born May 13, 1946 at Cervinara, Valle Caudina) immediately after the proof of the Riemann Hypothesis (Gallo’s RH-Mirabilis Theorem , released on the Web April 14, 2010.

By virtue of the Gallo’s RH-Mirabilis Theorem every non-trivial zero s = x + yi of the Riemann‘s zeta function is such that Re (z) = x = 1 / 2 = 0.5, for which both s = 0.5 + yi and its conjugated 1-s = 0.5-yi are nontrivial solutions of the Riemann’s zeta function. These zeros s and 1-s are infinite and are located symmetrically in relation to the “center of symmetry of Riemann” R0 = (1 / 2, 0) on the so-called critical line of the Riemann x = 1 /2. The proposed problem will be solved as soon as they were identified: a) a center of symmetry G0 = (xG, 0) on the real axis of the abscissa (y = 0), with appropriate xG ; b) a function g of symmetry of Gallo which involving biunivocally to any pair (s, (1 – s)) of non-trivial zeros of the Riemann’s zeta function the pair of real values of Gallo (g1, g2) , with g1 = g (s) and g2 = g (1-s) symmetrical to the real center of symmetry G0 of Gallo. This problem is solvable if and only if, the Hermitian matrix G of Gallo (which is an element of the overall group of grade 2 or GL2) is introduced consisting of the elements a11 = a22 = 1, a12 = 0.5 + s = yi , a22 = 1-s = 0.5-yi. Therefore, the Gallo characteristic polynomial associated with the G is given by the complex algebraic second-degree polynomial G (x, s) = x ^ 2-2x + (s ^ 2-s +1), 2 being the value of the trace of G. The solutions of the Gallo characteristic polynomial are the real zeros of Gallo g1= 1+ H and g2 = 1 – H with H = (√ (1 +4 yì2)) / 2 . It follows that, if we establish the two biunivocal correspondences: c1 : s complex number to g1 real number and c2 : s complex number to g2 real number, the problem is completely solved. In this way, in fact, the Gallo’s Hermitian operator G , by the roto-translation (π / 2, +1 / 2), means that the critical line of the Riemann x = 1 / 2 and the origin R0 =(1 / 2,0) of the symmetry of the Riemann’s non-trivial zeros and s 1-s they turn into, respectively, the real axis of the abscissa y = 0 (or the real line of Gallo) and the origin G0 = (1, 0) of the symmetry of Gallo real zeros g1 and g2.

And in fact c1 is such that to the nontrivial zeros of Riemann s = 0.5 + yi associates the Gallo’s real zeros g1 = 1 + H which are to the right of G0, while to non-trivial zeros of Riemann’s 1-s= 0.5 – yi the c2 associates the Gallo’s real zeros g2 = 1-H which are at the left of G0. For example to value s1=0.5 +i 14.134725… (first nontrivial zero of Riemann) the c1 associates biunivocally the first Gallo’s real zero G1 = 15. 143 565 7 …, while the to symmetric of s, i.e. 1-s = 0.5- i 14.134725 …, the c2 associates biunivocally the symmetric to G0 of the first Gallo’s real zero, ie G’1 = -13.143 565 7 … and, therefore, in general is g1=s +1 and g2 = – (s-1).

In light of the above, there is thus the following: THE CHARACTERISTIC THEOREM OF GALLO (on non-trivial zeros of Riemann)

“The non-trivial complex numbers s = x + yi and 1-s = x-yi are non-trivial zeros of the Riemann zeta function if, and only if, their corresponding on the Gallo real line are, respectively, g1 = 1+H and g2 = 1-H with H = (√ (1 +4 y^2)) / 2, i.e. the zeros of the Gallo characteristic polynomial G (x, s) = x ^ 2-2x + (s ^ 2-s +1), associated with the Gallo Hermitian matrix G.”

(The proof of this theorem, as we have shown, it is immediate from Re (s) = Re (1-s) = 1 / 2, which is true from the Gallo RH-Mirabilis Theorem ). Andrews courtesy of the author. ]]>

I am not a mathemacian but I haven`t read nothing al all on this…but if this thing is real it is really an historic achievement not only for mathematics but also for all the sciences in general (In fact,I believe that the Riemann hypothesis (when it will be definitively confirmed) will be very important in physics,too!!!).

So,please,if anybody knows anything interesting concerning this possible demostration of the Riemann hypothesis,let me know something.

Best wishes from Switzerland,

Dr.Kathrine M. ]]>

Finally a proof of the Riemann Hypothesis by the Italian mathematician Onofrio Gallo (b. may 13, 1946 in Cervinara, Caudina Valley- Italy) Of the 23 problems of Hilbert (Paris, 1900), the Riemann Hypothesis (or RH) is the eighth and “was” one of the most difficult to resolve.No coincidence that I wrote “was” because there are now well two proofs of (RH), both by the mathematician Onofrio Gallo (b. 1946 in Cervinara, Caudina Valley – Italy): the first (“indirect “or RH THEOREM OF GALLO and the second (“direct” or RH-MIRABILIS THEOREM OF GALLO Both demonstrations were deposited at the Norwegian Academy of Sciences and Letters . Therefore, from April 14, 2010, all books on RH, given the double Riemann hypothesis demonstration by the Italian mathematician Onofrio Gallo, must be updated. Both demonstrations obtained by Onofrio Gallo are based on its original mathematical discoveries The Gallo’s “indirect” Gallo proof of the RH dates back to 2004 is based on the function “fi” of Gallo, on the Gallo’s Principle of Unidentical , on the Second Principle of General Knowledge (in this case the principle of identity of polynomials), coded for the first time by the same Gallo and on the Mirabilis Theorem of Gallo by which the Italian mathematician December 27, 1993 (Rome) had obtained the first demonstration of such “direct” worldwide in just six pages, by a single author of the equally famous Fermat’s Last Theorem (FLT), where failed even to themselves A.J.Wiles and R.Taylor, authors of a “indirect” proof of the FLT, published in May 1995. The second proof of the RH-MIRABILIS THEOREM by Onofrio Gallo consists of just seven lines, so that its author said he had succeeded in coping with the ‘mystery of mysteries” (of the RH or Riemann hypothesis) using the “simplest of the simplest” of the theorems of mathematics. The elegant and surrounded by lightning demonstration of the RH-MIRABILIS THEOREM of Gallo gives ample reasons to those who have long predicted the likely demonstration dell’RH not part of a team of mathematicians, but most likely by a single mathematician who made use of new ideas, new theories and new theorems and that places itself as a true outsider against common lines of research directed to solving the ‘mystery of mysteries’. The RH-THEOREM mirabilis Gallo uses a well-known symmetry properties of Riemann nontrivial zeros of the Riemann zeta function (by some called “the monster”). Be right for the Riemann “monster”, Onofrio Gallo built the Gallo complex function of symmetry from a general solution or non-trivial zero of the “monster”, showing that any non-trivial complex zero z = x + iy (x, y “, real non-zero) of the Riemann zeta function (“the monster”) must be of the type z = 1 / 2 + iy, ie that for each such z, the real part of z must lie on the so-called Riemann “critical line” x = 1 / 2. The “impossible” undertaking was therefore made by the mathematician cervinarese by applying a “double symmetry. The first already discovered by Riemann in 1859 (if ζ (s) = 0, ζ (1-s) = 0, with s-s and a complex non-trivial zeros of Riemann). The second finding himself Onofrio Gallo in 1993 (Mirabilis Theorem Gallo, Dec 27, 1993, Rome). Personally I have never seen a mathematical revolution of this magnitude and I will help to spread the news of the news! Andrews, mathematician. ]]>

Thank you for finding this. We will look into it.

]]>I found a minor inconsistency in the paper. In section 2, you list the first few terms as 0,1,1,1,2,1,1,1. Later on, at the bottom of section 4.2, you list the “positions of 1’s” as 1,2,3,4,6,7,8,10,11,… It seems there’s some ambiguity: when the baron has 1 coin, does he need one weighing or zero weighings? You apparently chose the latter answer in section 2 and the former in 4.2.

I guess you “officially” went with the latter version because that’s how you submitted it to the Online Encyclopedia of Integer Sequences…

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