[{"department":[{"_id":"TiBr"}],"quality_controlled":"1","date_updated":"2026-07-16T08:36:20Z","article_type":"original","external_id":{"arxiv":["2406.09256"]},"researchdata_availability":"no","title":"Integral solutions to systems of diagonal equations","arxiv":1,"issue":"1","type":"journal_article","month":"01","publication":"Pacific Journal of Mathematics","volume":340,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0030-8730"],"eissn":["1945-5844"]},"oa_version":"Preprint","OA_type":"green","_id":"21242","page":"179-198","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."}],"year":"2026","article_processing_charge":"No","day":"01","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>.","ista":"Rome N, Yamagishi S. 2026. Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. 340(1), 179–198.","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.","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>.","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>","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>","short":"N. Rome, S. Yamagishi, Pacific Journal of Mathematics 340 (2026) 179–198."},"publication_status":"published","status":"public","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2406.09256","open_access":"1"}],"supplementarymaterial":"no","date_published":"2026-01-01T00:00:00Z","OA_place":"repository","publisher":"Mathematical Sciences Publishers","doi":"10.2140/pjm.2026.340.179","date_created":"2026-02-16T15:17:27Z","intvolume":"       340","author":[{"first_name":"Nick","last_name":"Rome","full_name":"Rome, Nick"},{"full_name":"Yamagishi, Shuntaro","last_name":"Yamagishi","first_name":"Shuntaro","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b"}],"das_tickbox":"0"}]