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Ordinary two-point Chowla correlations

Logarithmically weighted averages and ordinary averages have different targets.

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Understanding the problem

Read the background

Logarithmically weighted averages and ordinary averages have different targets. The ordinary result must control the final scale rather than aggregate many scales.

The forms are fixed. The result does not assert uniformity for growing coefficients or resolve every higher-order Chowla correlation; the Elliott statement has a nonpretentiousness hypothesis.

Why it matters

If correct, resolves the ordinary two-point target, rather than only its logarithmically averaged counterpart.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The forms are fixed. The result does not assert uniformity for growing coefficients or resolve every higher-order Chowla correlation; the Elliott statement has a nonpretentiousness hypothesis.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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