REVIEW 2 cited by
The Riemann hypothesis is true up to $3\cdot 10^{12}$
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We verify numerically, in a rigorous way using interval arithmetic, that the Riemann hypothesis is true up to height $3\cdot10^{12}$. That is, all zeroes $\beta + i\gamma$ of the Riemann zeta-function with $0<\gamma\leq 3\cdot 10^{12}$ have $\beta = 1/2$.
Forward citations
Cited by 2 Pith papers
-
An explicit uniform cubic wedge for consecutive Toeplitz minors of the Riemann xi coefficients
For every r ≥ 2 and k ≥ 10^18 r^3, the consecutive Toeplitz minor D_{r,k} of the Riemann xi coefficients is strictly positive, proved without using verified zeta zeros.
-
Explicit formula for the discrete Laplace transform of the M\"obius function, related special functions, and a criterion for the Riemann hypothesis
Under simple zeros, Φ(e^{-x})=Σ μ(n)e^{-nx} equals a zero sum plus trivial-zero series with a log term; O(x^{-1/2}) implies RH unconditionally.
Discussion (0). Continue with ORCID to comment.