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Sep19-05, 06:17 AM
Sci Advisor
HW Helper
P: 1,123
Let K be the set of all solutions that satisfy [itex]\zeta (s) = 0[/itex]. Let there exist some p such that:

[tex]\frac{\partial^2 p}{\partial i^2} a^3 - \Gamma (i^2) = 0[/tex]

Now I can prove that these exists a solution [itex]i = f_k (p)[/itex] therefore i exists. If i exists there must be a limit to g(p) and p approaches infinity and therefore p exists. Thus the roots of:

[tex]\int_0^\infty \frac{g(s)}{p \Gamma(s)} ds = \sin i[/tex]

Are synonyms to the Zeta functions roots and all have roots of [itex]\Re (p) = 1/2[/itex]

Therefore RH is proven and no one can come up with a counter-example.