E088: Zero counting via Riemann–von Mangoldt¶
E088: Zero counting via Riemann–von Mangoldt¶
Tags: analysis, quantitative-exploration, visualization, riemann-zeta, zeta-zeros, numerics
Highlights¶
Focused numeric experiment with a single main figure.
Parameters saved to
params.jsonfor reproducibility.Lightweight computation suitable for CI “slow” suite (small defaults).
What is computed¶
A parameterized numeric evaluation related to the Riemann zeta function.
A visualization summarizing the main phenomenon for the chosen parameter range.
Algorithm sketch¶
Build the numeric grid / sampling points.
Evaluate the target quantity with controlled truncation.
Render the figure and write a short report.
Outputs¶
report.md— short narrative summaryparams.json— experiment parameters snapshotfigures/fig_01_rvm_zero_counting.png— main figure
Published run snapshot¶
If this experiment is included in the docs gallery, include the published snapshot (report + params).
We compare the index n of the nth non-trivial zero with the Riemann–von Mangoldt main-term approximation. The difference should remain relatively small compared to n and reflects the lower-order terms and fluctuations.
params.json (snapshot)
{
"mp_dps": 70,
"n_zeros": 40
}