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The Riemann Hypothesis 
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#37
Jan1712, 04:19 AM

P: 399

http://www.youtube.com/watch?v=Oq7AIgrqCj8
the Riemann Xi function(s) [tex] \xi(1/2+z) [/tex] and [tex] \xi(1/2+iz) [/tex] can be expressed as a functional determinant of a Hamiltonian operator, functional determinants may be evaluated by zeta regularization, using in both cases the Theta functions , semiclassical and spectral ones :) 


#38
Jan2512, 07:33 AM

P: 399

[tex] \xi (s) = \xi(1s) [/tex] with [tex] \frac{\xi(s)}{\xi(0)}= \frac{det(H+1/4s(1s))}{det(H+1/4)} [/tex]
with [tex] H=  \partial _{x}^{2}+ f(x) [/tex] and [tex] f^{1}(x)= \frac{2}{\sqrt \pi }\frac{d^{1/2}{dx^{1/2}}Arg (1/2+i \sqrt x ) [/tex] http://vixra.org/abs/1111.0105 


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