Erdős and Kac: a Gaussian law for additive number-theoretic functions

What changed

Proved a Gaussian limiting law for normalized additive arithmetic functions including distinct prime-factor counts.

Scientific scope

The record is the exact two-author 1940 American Journal of Mathematics paper. It retains the paper's hypotheses and normalization and does not absorb the Hardy–Ramanujan precursor, the 1939 preliminary note or later quantitative refinements.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact two-author 1940 American Journal of Mathematics paper. It retains the paper's hypotheses and normalization and does not absorb the Hardy–Ramanujan precursor, the 1939 preliminary note or later quantitative refinements.

Contributors

• Paul Erdős · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.
• Mark Kac · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Erdős archive copy of Gaussian-law paper
• JSTOR DOI for Erdős–Kac paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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