{"title":"椭圆多项式零点的期望能量","authors":"Víctor de la Torre, Jordi Marzo","doi":"10.1007/s00365-024-09684-2","DOIUrl":null,"url":null,"abstract":"<p>In 2011, Armentano, Beltrán and Shub obtained a closed expression for the expected logarithmic energy of the random point process on the sphere given by the roots of random elliptic polynomials. We consider a different approach which allows us to extend the study to the Riesz energies and to compute the expected separation distance.\n</p>","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":"1 1","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Expected Energy of Zeros of Elliptic Polynomials\",\"authors\":\"Víctor de la Torre, Jordi Marzo\",\"doi\":\"10.1007/s00365-024-09684-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In 2011, Armentano, Beltrán and Shub obtained a closed expression for the expected logarithmic energy of the random point process on the sphere given by the roots of random elliptic polynomials. We consider a different approach which allows us to extend the study to the Riesz energies and to compute the expected separation distance.\\n</p>\",\"PeriodicalId\":50621,\"journal\":{\"name\":\"Constructive Approximation\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Constructive Approximation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00365-024-09684-2\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Constructive Approximation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00365-024-09684-2","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In 2011, Armentano, Beltrán and Shub obtained a closed expression for the expected logarithmic energy of the random point process on the sphere given by the roots of random elliptic polynomials. We consider a different approach which allows us to extend the study to the Riesz energies and to compute the expected separation distance.
期刊介绍：
Constructive Approximation is an international mathematics journal dedicated to Approximations and Expansions and related research in computation, function theory, functional analysis, interpolation spaces and interpolation of operators, numerical analysis, space of functions, special functions, and applications.
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