Chebyshev Partition function: A connection between Statistical Physics and Riemann Hypothesis

Details Chebyshev Partition function: A connection between Statistical Physics and Riemann Hypothesis Chebyshev Partition function: A connection between Statistical Physics and Riemann Hypothesis

2006-07-04

arxiv.org/abs/math/0607095v5

Mathematics

General Mathematics

This submission has been withdrawn by arXiv administrators because of fraudulently claimed institutional affiliation and statu

Scientific paper

In this paper we present a method to obtain a possible self-adjoint Hamiltonian operator so its energies satisfy Z(1/2+iE_n)=0, which is an statement equivalent to Riemann Hypothesis, first we use the explicit formula for the Chebyshev function Psi(x) and apply the change x=exp(u), after that we consider an Statistical partition function involving the Chebyshev function and its derivative so Z=Tr(exp(-BH), from the integral definition of the partition function Z we try to obtain the Hamiltonian operator assuming that H=P^{2}+V(x) by proposing a Non-linear integral equation involving Z(B=-iu) and V(x).

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