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Fungrim entry: e6ff64

Re ⁣(ρn)=12\operatorname{Re}\!\left(\rho_{n}\right) = \frac{1}{2}
Assumptions:nZ  and  n0  and  (n<103800788359  or  RH)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}(z) 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), 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"))

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

2020-04-08 16:14:44.404316 UTC