@article{AKK,
 author = {Arango-Pi{\~n}eros, Santiago and Keliher, Daniel and Keyes, Christopher},
 title = {{Mertens}' theorem for {Chebotarev} sets},
 journal = {International Journal of Number Theory},
 volume = {18}, number = {8}, pages = {1823--1842}, year = {2022},
 note = {\href{https://doi.org/10.1142/S1793042122500932}{doi:10.1142/S1793042122500932}. Theorem A is cited from \href{https://arxiv.org/abs/2103.14747v2}{arXiv:2103.14747v2} (2021)}
}
@article{Fish,
 author = {Fish, Alexander},
 title = {Random {Liouville} functions and normal sets},
 journal = {Acta Arithmetica},
 volume = {120}, number = {2}, pages = {191--196}, year = {2005},
 note = {\href{https://doi.org/10.4064/aa120-2-6}{doi:10.4064/aa120-2-6}. \href{https://arxiv.org/abs/math/0509315}{arXiv:math/0509315}}
}
@article{GHR,
 author = {Galatolo, Stefano and Hoyrup, Mathieu and Rojas, Crist{\'o}bal},
 title = {A constructive {Borel--Cantelli} lemma. {Constructing} orbits with required statistical properties},
 journal = {Theoretical Computer Science},
 volume = {410}, number = {21--23}, pages = {2207--2222}, year = {2009},
 note = {\href{https://doi.org/10.1016/j.tcs.2009.02.010}{doi:10.1016/j.tcs.2009.02.010}. \href{https://arxiv.org/abs/0711.1478}{arXiv:0711.1478}}
}
@misc{Kedlaya,
 author = {Kedlaya, Kiran S.},
 title = {Notes on analytic number theory},
 howpublished = {Online lecture notes},
 note = {\href{https://kskedlaya.org/ant/chap-primes-in-ap.html}{Section 4.4, Theorem 4.12}; \href{https://kskedlaya.org/ant/chap-selberg.html}{Section 13.2, equations (13.2.3)--(13.2.4)}; chapter URL: \url{https://kskedlaya.org/ant/chap-selberg.html}. Edition consulted 28 September 2026}
}
@article{Klurman,
 author = {Klurman, Oleksiy},
 title = {Correlations of multiplicative functions and applications},
 journal = {Compositio Mathematica},
 volume = {153}, number = {8}, pages = {1622--1657}, year = {2017},
 note = {\href{https://doi.org/10.1112/S0010437X17007163}{doi:10.1112/S0010437X17007163}. Lemma 2.1 and Proposition 1.1 are cited from \href{https://arxiv.org/abs/1603.08453v1}{arXiv:1603.08453v1} (2016)}
}
@article{KMT,
 author = {Klurman, Oleksiy and Mangerel, Alexander P. and Ter{\"a}v{\"a}inen, Joni},
 title = {On {Elliott}'s conjecture and applications},
 journal = {Proceedings of the London Mathematical Society},
 volume = {133}, number = {3}, pages = {e70205}, year = {2026},
 note = {\href{https://doi.org/10.1112/plms.70205}{doi:10.1112/plms.70205}. Theorem numbering refers to \href{https://arxiv.org/abs/2304.05344v2}{arXiv:2304.05344v2} (2023), not the publisher's edition}
}
@misc{Milne,
 author = {Milne, James S.},
 title = {Fields and {Galois} theory},
 year = {2022},
 note = {Version 5.10, 144 pp. Galois groups over $\mathbb Q$, pp. 55--57; cyclotomic extensions, pp. 64--67; norms and traces, pp. 82--85. \href{https://www.jmilne.org/math/CourseNotes/FT.pdf}{Author's lecture notes}. Stable index: \url{https://www.jmilne.org/math/CourseNotes/ft.html}}
}
@misc{NIST,
 author = {{National Institute of Standards and Technology}},
 title = {{Digital Library of Mathematical Functions}},
 note = {\href{https://dlmf.nist.gov/27.9}{Section 27.9} (quadratic reciprocity); \href{https://dlmf.nist.gov/27.11}{equations (27.11.9) and (27.11.11)} (prime sums in progressions); \href{https://dlmf.nist.gov/27.12.E8}{equation (27.12.8)} (prime counts). Online edition consulted 28 September 2026; only fixed moduli are used}
}
@article{PollioRapinchuk,
 author = {Pollio, Timothy P. and Rapinchuk, Andrei S.},
 title = {The multinorm principle for linearly disjoint {Galois} extensions},
 journal = {Journal of Number Theory},
 volume = {133}, number = {2}, pages = {802--821}, year = {2013},
 note = {\href{https://doi.org/10.1016/j.jnt.2012.07.014}{doi:10.1016/j.jnt.2012.07.014}. \href{https://arxiv.org/abs/1203.0359}{arXiv:1203.0359}}
}
@misc{PoulyNoise,
 author = {Pouly, Brice},
 title = {Prime noise, polynomial observations and trace-preserving completion of multiplicative functions},
 year = {2026},
 doi = {10.5281/zenodo.22959769},
 note = {Author's manuscript, 25 September 2026, 22 pp. \href{https://doi.org/10.5281/zenodo.22959769}{doi:10.5281/zenodo.22959769}. Theorem 1.1, Corollary 5.3, Theorems 6.1--6.2 and Proposition 8.1}
}

@article{Najnudel,
 author = {Najnudel, Joseph},
 title = {On consecutive values of random completely multiplicative functions},
 journal = {Electronic Journal of Probability},
 volume = {25}, pages = {1--28}, year = {2020},
 note = {Article 59. \href{https://doi.org/10.1214/20-EJP456}{doi:10.1214/20-EJP456}. Proposition 6.3 is cited from \href{https://arxiv.org/abs/1702.01470v2}{arXiv:1702.01470v2}}
}
@article{KSX,
 author = {Klurman, Oleksiy and Shkredov, Ilya D. and Xu, Max Wenqiang},
 title = {On the random {Chowla} conjecture},
 journal = {Geometric and Functional Analysis},
 volume = {33}, number = {3}, pages = {749--777}, year = {2023},
 note = {\href{https://doi.org/10.1007/s00039-023-00641-y}{doi:10.1007/s00039-023-00641-y}. Theorem 1.1 and Proposition 1.4 are cited from \href{https://arxiv.org/abs/2202.08767v2}{arXiv:2202.08767v2}}
}
@article{WangXu,
 author = {Wang, Victor Y. and Xu, Max Wenqiang},
 title = {Paucity phenomena for polynomial products},
 journal = {Bulletin of the London Mathematical Society},
 volume = {56}, number = {8}, pages = {2718--2726}, year = {2024},
 note = {\href{https://doi.org/10.1112/blms.13095}{doi:10.1112/blms.13095}. Theorem 1.1 and Section 1.3 are cited from \href{https://arxiv.org/abs/2211.02908v2}{arXiv:2211.02908v2}}
}
@article{ChinisShala,
 author = {Chinis, Jake and Shala, Besfort},
 title = {Random {Chowla}'s conjecture for {Rademacher} multiplicative functions},
 journal = {Transactions of the American Mathematical Society},
 volume = {378}, number = {11}, pages = {8025--8053}, year = {2025},
 note = {\href{https://doi.org/10.1090/tran/9457}{doi:10.1090/tran/9457}. Theorem 1.2 and Section 1.4 are cited from \href{https://arxiv.org/abs/2409.05952v2}{arXiv:2409.05952v2}}
}
@misc{DBWX,
 author = {de la Bret{\`e}che, R{\'e}gis and Wang, Victor Y. and Xu, Max Wenqiang},
 title = {Random multiplicative functions and making squares from polynomial values},
 year = {2026},
 note = {Preprint, 7 July 2026. \href{https://arxiv.org/abs/2607.06398v1}{arXiv:2607.06398v1}. Theorem 1.2 is cited for comparison}
}
@article{BerendBilu,
 author = {Berend, Daniel and Bilu, Yuri},
 title = {Polynomials with roots modulo every integer},
 journal = {Proceedings of the American Mathematical Society},
 volume = {124}, number = {6}, pages = {1663--1671}, year = {1996},
 note = {\href{https://doi.org/10.1090/S0002-9939-96-03210-8}{doi:10.1090/S0002-9939-96-03210-8}. Theorem 2; see also \cite[Theorem 2.1]{EKT}}
}
@article{EKT,
 author = {Elsholtz, Christian and Klahn, Benjamin and Technau, Marc},
 title = {On polynomials with roots modulo almost all primes},
 journal = {Acta Arithmetica},
 volume = {205}, number = {3}, pages = {251--263}, year = {2022},
 note = {\href{https://doi.org/10.4064/aa220407-9-7}{doi:10.4064/aa220407-9-7}. Theorem 2.1 and Proposition 2.2 are cited from \href{https://arxiv.org/abs/2206.13466v2}{arXiv:2206.13466v2}}
}