# 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"))

## Topics using this entry

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

2021-03-15 19:12:00.328586 UTC