{"title":"关于复多项式及其衍生物","authors":"Prasanna Kumar","doi":"10.7546/crabs.2023.11.01","DOIUrl":null,"url":null,"abstract":"In this paper, we prove some Turán-type inequalities for the polynomials all of whose zeros lie on a ray emanating from the origin, or symmetrically placed along this ray and having all their zeros in $$|z|\\leq K$$, $$K\\geq 1$$. Our results are the best possible, and examples of equality cases have been presented.","PeriodicalId":104760,"journal":{"name":"Proceedings of the Bulgarian Academy of Sciences","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a Complex Polynomial and Its Derivative\",\"authors\":\"Prasanna Kumar\",\"doi\":\"10.7546/crabs.2023.11.01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove some Turán-type inequalities for the polynomials all of whose zeros lie on a ray emanating from the origin, or symmetrically placed along this ray and having all their zeros in $$|z|\\\\leq K$$, $$K\\\\geq 1$$. Our results are the best possible, and examples of equality cases have been presented.\",\"PeriodicalId\":104760,\"journal\":{\"name\":\"Proceedings of the Bulgarian Academy of Sciences\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Bulgarian Academy of Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/crabs.2023.11.01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Bulgarian Academy of Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/crabs.2023.11.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we prove some Turán-type inequalities for the polynomials all of whose zeros lie on a ray emanating from the origin, or symmetrically placed along this ray and having all their zeros in $$|z|\leq K$$, $$K\geq 1$$. Our results are the best possible, and examples of equality cases have been presented.
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