Riemann Hypothesis — Zeta Explorer

Educational lab notebook for ζ(s), the critical line, and safe partial-sum experiments.

math number-theory complex notebook

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What this template does

This is a ready-to-run GetCalcMaster Notebook starter. Open it into Notebook, run once with defaults, then tweak inputs and keep your assumptions next to the math.

How to use it (recommended)

Open in Notebook.
Read the first text cell: scope + numerical caveats.
Run the default exploration once (baseline).
Adjust the sampling range/step size; rerun and compare.
Snapshot your best run with parameters and caveats recorded.

Tip: When a result matters, verify it twice: a unit check + a second method (graph/estimate).

Preview (first cells)

This preview is for readability. The full template loads into Notebook when you click Open.

TEXT

# Riemann Hypothesis — Zeta Explorer
This is an educational lab notebook. It does **not** prove the Riemann Hypothesis.

For the full add-on page (with a one-click generator):
/addons/riemann-hypothesis

MATH

# ζ(2) partial sum demo (N=20)
zeta2_N20 = 1/(1^(2)) + 1/(2^(2)) + 1/(3^(2)) + 1/(4^(2)) + 1/(5^(2)) + 1/(6^(2)) + 1/(7^(2)) + 1/(8^(2)) + 1/(9^(2)) + 1/(10^(2)) + 1/(11^(2)) + 1/(12^(2)) + 1/(13^(2)) + 1/(14^(2)) + 1/(15^(2)) + 1/(16^(2)) + 1/(17^(2)) + 1/(18^(2)) + 1/(19^(2)) + 1/(20^(2))

MATH

zeta2_exact = pi^2/6

MATH

zeta2_err = zeta2_N20 - zeta2_exact

MATH

# ζ(4) partial sum demo (N=20)
zeta4_N20 = 1/(1^(4)) + 1/(2^(4)) + 1/(3^(4)) + 1/(4^(4)) + 1/(5^(4)) + 1/(6^(4)) + 1/(7^(4)) + 1/(8^(4)) + 1/(9^(4)) + 1/(10^(4)) + 1/(11^(4)) + 1/(12^(4)) + 1/(13^(4)) + 1/(14^(4)) + 1/(15^(4)) + 1/(16^(4)) + 1/(17^(4)) + 1/(18^(4)) + 1/(19^(4)) + 1/(20^(4))

MATH

zeta4_exact = pi^4/90