薄集上具有随机系数的同次多项式的局部溶解度

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2024-09-30 DOI:10.1112/mtk.12282

Heejong Lee, Seungsu Lee, Kiseok Yeon

{"title":"薄集上具有随机系数的同次多项式的局部溶解度","authors":"Heejong Lee, Seungsu Lee, Kiseok Yeon","doi":"10.1112/mtk.12282","DOIUrl":null,"url":null,"abstract":"Let <math></math> and <math></math> be natural numbers greater or equal to 2. Let <math></math> be a homogeneous polynomial in <math></math> variables of degree <math></math> with integer coefficients <math></math>, where <math></math> denotes the inner product, and <math></math> denotes the Veronese embedding with <math></math>. Consider a variety <math></math> in <math></math>, defined by <math></math>. In this paper, we examine a set of integer vectors <math></math>, defined by\n\n ","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The local solubility for homogeneous polynomials with random coefficients over thin sets\",\"authors\":\"Heejong Lee, Seungsu Lee, Kiseok Yeon\",\"doi\":\"10.1112/mtk.12282\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <math></math> and <math></math> be natural numbers greater or equal to 2. Let <math></math> be a homogeneous polynomial in <math></math> variables of degree <math></math> with integer coefficients <math></math>, where <math></math> denotes the inner product, and <math></math> denotes the Veronese embedding with <math></math>. Consider a variety <math></math> in <math></math>, defined by <math></math>. In this paper, we examine a set of integer vectors <math></math>, defined by\\n\\n \",\"PeriodicalId\":18463,\"journal\":{\"name\":\"Mathematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematika\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12282\",\"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":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12282","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设和为大于或等于 2 的自然数，设为变量中的同次多项式，其系数为整数，其中表示内积，表示与的维罗内嵌。考虑由 .在本文中，我们研究一组整数向量，其定义如下

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The local solubility for homogeneous polynomials with random coefficients over thin sets

Let and be natural numbers greater or equal to 2. Let be a homogeneous polynomial in variables of degree with integer coefficients , where denotes the inner product, and denotes the Veronese embedding with . Consider a variety in , defined by . In this paper, we examine a set of integer vectors , defined by

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.