# E120: Liouville λ(n): partial sums and parity

```{figure} ../_static/experiments/e120_hero.png
:alt: E120 hero
:class: experiment-hero

E120: Liouville λ(n): partial sums and parity
```

**Tags:** `number-theory`, `quantitative-exploration`, `visualization`, `liouville`, `omega`

## Highlights

- Focused numeric experiment with a small set of figures.
- Parameters saved to `params.json` for reproducibility.
- Defaults are chosen, so the experiment remains feasible for the CI “slow” suite.

## What is computed

- Explore partial sums of the Liouville function and simple parity correlations.

## Notes

- This page summarizes the intent; see the generated `report.md` in `out/` for concrete outputs.

## Published run snapshot

If this experiment is included in the docs gallery, include the published snapshot (report + params).

```{include} ../reports/e120.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

::: {dropdown} params.json (snapshot)
:open:

```{literalinclude} ../params/e120.json
:language: json
```

:::

## References

- See the arithmetic-functions background pages in `docs/background/`.

## Related experiments

- {doc}`e056` (Liouville vs. Möbius walks)
- {doc}`e066` (Character partial sums: cancellation profiles.)
- {doc}`e078` (Max partial sums across characters.)
- {doc}`e110` (E110: Dirichlet L-series partial sums at s=1 and s=1/2)
- {doc}`e057` (Erdős–Kac in practice)