Liouville function, von Mangoldt function, and norm forms at random binary forms Diao, Yijie ; https://orcid.org/0000-0002-4989-5330 ddc:500 We analyze the average behavior of various arithmetic functions at the values of degree 𝑑 binary forms ordered by height, with probability 1. This approach yields averaged versions of the Chowla conjecture and the Bateman–Horn conjecture for random binary forms. Furthermore, we show that the rational Hasse principle holds for almost all Châtelet varieties defined by a fixed norm form of degree 𝑒 and by varying binary forms of fixed degree 𝑑, provided 𝑒 divides 𝑑. This proves an average version of a conjecture of Colliot-Thélène. Cambridge University Press 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22644 Diao Y. Liouville function, von Mangoldt function, and norm forms at random binary forms. <i>Glasgow Mathematical Journal</i>. 2026:1-34. doi:<a href="https://doi.org/10.1017/s0017089526101074">10.1017/s0017089526101074</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1017/s0017089526101074 info:eu-repo/semantics/altIdentifier/issn/0017-0895 info:eu-repo/semantics/altIdentifier/e-issn/1469-509X info:eu-repo/semantics/altIdentifier/arxiv/2506.18065 info:eu-repo/semantics/openAccess