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Fungrim entry: e6ff64

Re ⁣(ρn)=12\operatorname{Re}\!\left(\rho_{n}\right) = \frac{1}{2}
Assumptions:nZandn0and(n<103800788359orRH)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
ReRe ⁣(z)\operatorname{Re}\!\left(z\right) Real part
RiemannZetaZeroρn\rho_{n} Nontrivial zero of the Riemann zeta function
ZZZ\mathbb{Z} Integers
Absz\left|z\right| Absolute value
RiemannHypothesisRH\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), Unequal(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"))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC