{"title":"在 Q2$\\mathbb {Q}_2$ 的完全夯实扩展上的两倍奇数度加法形式的可溶性","authors":"Drew Duncan","doi":"10.1112/blms.13120","DOIUrl":null,"url":null,"abstract":"<p>We prove that an additive form of degree <span></span><math>\n <semantics>\n <mrow>\n <mi>d</mi>\n <mo>=</mo>\n <mn>2</mn>\n <mi>m</mi>\n </mrow>\n <annotation>$d=2m$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <mi>m</mi>\n <annotation>$m$</annotation>\n </semantics></math> odd over any totally ramified extension of <span></span><math>\n <semantics>\n <msub>\n <mi>Q</mi>\n <mn>2</mn>\n </msub>\n <annotation>$\\mathbb {Q}_2$</annotation>\n </semantics></math> has a nontrivial zero if the number of variables <span></span><math>\n <semantics>\n <mi>s</mi>\n <annotation>$s$</annotation>\n </semantics></math> satisfies <span></span><math>\n <semantics>\n <mrow>\n <mi>s</mi>\n <mo>⩾</mo>\n <mfrac>\n <msup>\n <mi>d</mi>\n <mn>2</mn>\n </msup>\n <mn>4</mn>\n </mfrac>\n <mo>+</mo>\n <mn>3</mn>\n <mi>d</mi>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$s \\geqslant \\frac{d^2}{4} + 3d + 1$</annotation>\n </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 10","pages":"3129-3133"},"PeriodicalIF":0.8000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solubility of additive forms of twice odd degree over totally ramified extensions of \\n \\n \\n Q\\n 2\\n \\n $\\\\mathbb {Q}_2$\",\"authors\":\"Drew Duncan\",\"doi\":\"10.1112/blms.13120\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove that an additive form of degree <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>d</mi>\\n <mo>=</mo>\\n <mn>2</mn>\\n <mi>m</mi>\\n </mrow>\\n <annotation>$d=2m$</annotation>\\n </semantics></math>, <span></span><math>\\n <semantics>\\n <mi>m</mi>\\n <annotation>$m$</annotation>\\n </semantics></math> odd over any totally ramified extension of <span></span><math>\\n <semantics>\\n <msub>\\n <mi>Q</mi>\\n <mn>2</mn>\\n </msub>\\n <annotation>$\\\\mathbb {Q}_2$</annotation>\\n </semantics></math> has a nontrivial zero if the number of variables <span></span><math>\\n <semantics>\\n <mi>s</mi>\\n <annotation>$s$</annotation>\\n </semantics></math> satisfies <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>s</mi>\\n <mo>⩾</mo>\\n <mfrac>\\n <msup>\\n <mi>d</mi>\\n <mn>2</mn>\\n </msup>\\n <mn>4</mn>\\n </mfrac>\\n <mo>+</mo>\\n <mn>3</mn>\\n <mi>d</mi>\\n <mo>+</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$s \\\\geqslant \\\\frac{d^2}{4} + 3d + 1$</annotation>\\n </semantics></math>.</p>\",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"56 10\",\"pages\":\"3129-3133\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/blms.13120\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13120","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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