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PreprintarXiv licencearXiv

Dynamical generalizations of the two-point Chowla conjecture

  • Biao Wang
  • Shaoyun Yi
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Abstract

In 1965, Chowla conjectured that the values of the Liouville function become asymptotically uncorrelated at consecutive natural numbers. Recently, the two-point case is resolved by OpenAI. In 2026, Charamaras and Richter conjectured a generalization of the Chowla conjecture to the asymptotic independence of the consecutive prime Omega functions. In this article, we prove the two-point case of their conjecture. As a consequence, we obtain a dynamical generalization of the two-point Chowla conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026dynamical,
  title = {{Dynamical generalizations of the two-point Chowla conjecture}},
  author = {Biao Wang and Shaoyun Yi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16394},
  eprint = {2610.16394},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16394},
}
RIS
TY  - UNPB
TI  - Dynamical generalizations of the two-point Chowla conjecture
AU  - Biao Wang
AU  - Shaoyun Yi
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16394
UR  - https://arxiv.org/abs/2610.16394
AB  - In 1965, Chowla conjectured that the values of the Liouville function become asymptotically uncorrelated at consecutive natural numbers. Recently, the two-point case is resolved by OpenAI. In 2026, Charamaras and Richter conjectured a generalization of the Chowla conjecture to the asymptotic independence of the consecutive prime Omega functions. In this article, we prove the two-point case of their conjecture. As a consequence, we obtain a dynamical generalization of the two-point Chowla conjecture.
ER  -