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nt.quantity concept – Why doesn’t a zeta zero counting responsibility $N_0(T)$ behave precisely in a neighborhood that every one violations of Gram’s regulation are occurred? retort

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nt.quantity concept – Why doesn’t a zeta zero counting responsibility $N_0(T)$ behave precisely in a neighborhood that every one violations of Gram’s regulation are occurred?

Q: Why doesn’t a zeta zero counting responsibility, on the captious line, $N_0(T)=1+frac{vartheta(T)}{pi}+frac{arg(zeta(frac12+i T))}{pi}$ behave precisely in a neighborhood that every one violations of Gram’s regulation are occurred?

$N_0(T)=1-frac{Tlog(2pi)}{2pi}-frac{1}{2pi i}left(logGamma(frac12-i T)-log(zeta(frac12+i T))+logleft(frac{zeta(frac12+i T)}{(2pi)^{i t}Gamma(frac12-i T)}capable)capable)$,

$N_0′(T)=0$ and

$int{N_0(T)}{dT}=T N_0(T)$,

the place $N_0(t)$ is a differentiable and integrable design on the symbolic computation.

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