{"oa_version":"Preprint","month":"08","OA_place":"repository","type":"preprint","department":[{"_id":"TiBr"}],"author":[{"first_name":"Jakob","last_name":"Glas","full_name":"Glas, Jakob","id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb"},{"first_name":"Leonhard","last_name":"Hochfilzer","full_name":"Hochfilzer, Leonhard"}],"article_processing_charge":"No","date_published":"2022-08-10T00:00:00Z","_id":"18293","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","doi":"10.48550/arXiv.2208.05422","date_updated":"2024-10-11T09:44:22Z","language":[{"iso":"eng"}],"title":"On a question of Davenport and diagonal cubic forms over Fq(t)","oa":1,"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"18132"}]},"day":"10","citation":{"ama":"Glas J, Hochfilzer L. On a question of Davenport and diagonal cubic forms over Fq(t). <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2208.05422\">10.48550/arXiv.2208.05422</a>","ieee":"J. Glas and L. Hochfilzer, “On a question of Davenport and diagonal cubic forms over Fq(t),” <i>arXiv</i>. .","short":"J. Glas, L. Hochfilzer, ArXiv (n.d.).","mla":"Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal Cubic Forms over Fq(T).” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2208.05422\">10.48550/arXiv.2208.05422</a>.","chicago":"Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal Cubic Forms over Fq(T).” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2208.05422\">https://doi.org/10.48550/arXiv.2208.05422</a>.","apa":"Glas, J., &#38; Hochfilzer, L. (n.d.). On a question of Davenport and diagonal cubic forms over Fq(t). <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2208.05422\">https://doi.org/10.48550/arXiv.2208.05422</a>","ista":"Glas J, Hochfilzer L. On a question of Davenport and diagonal cubic forms over Fq(t). arXiv, <a href=\"https://doi.org/10.48550/arXiv.2208.05422\">10.48550/arXiv.2208.05422</a>."},"publication":"arXiv","corr_author":"1","publication_status":"submitted","abstract":[{"lang":"eng","text":"Given a non-singular diagonal cubic hypersurface X⊂Pn−1 over Fq(t) with char(Fq)≠3, we show that the number of rational points of height at most |P| is O(|P|3+ε) for n=6 and O(|P|2+ε) for n=4. In fact, if n=4 and char(Fq)>3 we prove that the number of rational points away from any rational line contained in X is bounded by O(|P|3/2+ε). From the result in 6 variables we deduce weak approximation for diagonal cubic hypersurfaces for n≥7 over Fq(t) when char(Fq)>3 and handle Waring's problem for cubes in 7 variables over Fq(t) when char(Fq)≠3. Our results answer a question of Davenport regarding the number of solutions of bounded height to x31+x32+x33=x34+x35+x36 with xi∈Fq[t]."}],"external_id":{"arxiv":["2208.05422"]},"year":"2022","date_created":"2024-10-10T12:46:41Z","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2208.05422","open_access":"1"}]}