{"date_created":"2026-02-16T15:17:27Z","page":"179-198","supplementarymaterial":"no","type":"journal_article","arxiv":1,"article_processing_charge":"No","_id":"21242","das_tickbox":"0","intvolume":"       340","researchdata_availability":"no","issue":"1","doi":"10.2140/pjm.2026.340.179","publication_identifier":{"issn":["0030-8730"],"eissn":["1945-5844"]},"date_updated":"2026-07-16T08:36:20Z","date_published":"2026-01-01T00:00:00Z","title":"Integral solutions to systems of diagonal equations","abstract":[{"lang":"eng","text":"We obtain an asymptotic formula for the number of integral solutions to a system of diagonal equations. We obtain an asymptotic formula for the number of solutions with variables restricted to smooth numbers as well. We improve the required number of variables compared to previous results by incorporating recent progress on Waring’s problem and the resolution of the main conjecture in Vinogradov’s mean value theorem."}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2406.09256"}],"publication_status":"published","publication":"Pacific Journal of Mathematics","oa":1,"language":[{"iso":"eng"}],"OA_place":"repository","author":[{"last_name":"Rome","first_name":"Nick","full_name":"Rome, Nick"},{"last_name":"Yamagishi","first_name":"Shuntaro","full_name":"Yamagishi, Shuntaro","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b"}],"quality_controlled":"1","year":"2026","OA_type":"green","oa_version":"Preprint","publisher":"Mathematical Sciences Publishers","status":"public","day":"01","article_type":"original","department":[{"_id":"TiBr"}],"month":"01","volume":340,"external_id":{"arxiv":["2406.09256"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"mla":"Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” <i>Pacific Journal of Mathematics</i>, vol. 340, no. 1, Mathematical Sciences Publishers, 2026, pp. 179–98, doi:<a href=\"https://doi.org/10.2140/pjm.2026.340.179\">10.2140/pjm.2026.340.179</a>.","short":"N. Rome, S. Yamagishi, Pacific Journal of Mathematics 340 (2026) 179–198.","ama":"Rome N, Yamagishi S. Integral solutions to systems of diagonal equations. <i>Pacific Journal of Mathematics</i>. 2026;340(1):179-198. doi:<a href=\"https://doi.org/10.2140/pjm.2026.340.179\">10.2140/pjm.2026.340.179</a>","chicago":"Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers, 2026. <a href=\"https://doi.org/10.2140/pjm.2026.340.179\">https://doi.org/10.2140/pjm.2026.340.179</a>.","ieee":"N. Rome and S. Yamagishi, “Integral solutions to systems of diagonal equations,” <i>Pacific Journal of Mathematics</i>, vol. 340, no. 1. Mathematical Sciences Publishers, pp. 179–198, 2026.","apa":"Rome, N., &#38; Yamagishi, S. (2026). Integral solutions to systems of diagonal equations. <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pjm.2026.340.179\">https://doi.org/10.2140/pjm.2026.340.179</a>","ista":"Rome N, Yamagishi S. 2026. Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. 340(1), 179–198."}}