Fungrim entry: e6ff64

\operatorname{Re}\!\left(\rho_{n}\right) = \frac{1}{2}

Assumptions:

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \ne 0 \;\mathbin{\operatorname{and}}\; \left(\left|n\right| < 103800788359 \;\mathbin{\operatorname{or}}\; \operatorname{RH}\right)

References:

D. J. Platt (2016), Isolating some non-trivial zeros of zeta, Mathematics of Computation 86(307):1, DOI: 10.1090/mcom/3198

TeX:

\operatorname{Re}\!\left(\rho_{n}\right) = \frac{1}{2}

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \ne 0 \;\mathbin{\operatorname{and}}\; \left(\left|n\right| < 103800788359 \;\mathbin{\operatorname{or}}\; \operatorname{RH}\right)

Definitions:

Fungrim symbol	Notation	Short description
`Re`	$\operatorname{Re}(z)$	Real part
`RiemannZetaZero`	$\rho_{n}$	Nontrivial zero of the Riemann zeta function
`ZZ`	$\mathbb{Z}$	Integers
`Abs`	$\left\|z\right\|$	Absolute value
`RiemannHypothesis`	$\operatorname{RH}$	Riemann hypothesis

Source code for this entry:

Entry(ID("e6ff64"),
    Formula(Equal(Re(RiemannZetaZero(n)), Div(1, 2))),
    Variables(n),
    Assumptions(And(Element(n, ZZ), NotEqual(n, 0), Or(Less(Abs(n), 103800788359), RiemannHypothesis))),
    References("D. J. Platt (2016), Isolating some non-trivial zeros of zeta, Mathematics of Computation 86(307):1, DOI: 10.1090/mcom/3198"))

Fungrim entry: e6ff64

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