{"title":"确定具有前五个系数的 monal 形式的普遍性","authors":"Dayoon Park","doi":"10.1007/s11139-024-00849-y","DOIUrl":null,"url":null,"abstract":"<p>We classify the <span>\\((a_1,a_2,a_3,a_4,a_5)\\)</span> for which the universality of an <i>m</i>-gonal form <span>\\(F_m({\\textbf{x}})\\)</span> whose first five coefficients are <span>\\((a_1,a_2,a_3,a_4,a_5)\\)</span> is characterized as the representabilitiy of positive integers up to <span>\\(m-4\\)</span> and discuss some applications.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"111 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Determining universality of m-gonal forms with first five coefficients\",\"authors\":\"Dayoon Park\",\"doi\":\"10.1007/s11139-024-00849-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We classify the <span>\\\\((a_1,a_2,a_3,a_4,a_5)\\\\)</span> for which the universality of an <i>m</i>-gonal form <span>\\\\(F_m({\\\\textbf{x}})\\\\)</span> whose first five coefficients are <span>\\\\((a_1,a_2,a_3,a_4,a_5)\\\\)</span> is characterized as the representabilitiy of positive integers up to <span>\\\\(m-4\\\\)</span> and discuss some applications.</p>\",\"PeriodicalId\":501430,\"journal\":{\"name\":\"The Ramanujan Journal\",\"volume\":\"111 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Ramanujan Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11139-024-00849-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00849-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们将前五个系数为 \((a_1,a_2,a_3,a_4,a_5)\)的 m-gonal form \(F_m({\textbf{x}})\)的普遍性归类为 \((a_1,a_2,a_3,a_4,a_5)\)，并讨论了一些应用。
Determining universality of m-gonal forms with first five coefficients
We classify the \((a_1,a_2,a_3,a_4,a_5)\) for which the universality of an m-gonal form \(F_m({\textbf{x}})\) whose first five coefficients are \((a_1,a_2,a_3,a_4,a_5)\) is characterized as the representabilitiy of positive integers up to \(m-4\) and discuss some applications.
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