{"title":"具有指数算术序列的完整函数","authors":"Dallas Ruth, Khang Tran","doi":"arxiv-2408.02096","DOIUrl":null,"url":null,"abstract":"For a given entire function $f(z)=\\sum_{j=0}^{\\infty}a_{j}z^{j}$, we study\nthe zero distribution of $f_{r}(z)=\\sum_{j\\equiv r\\pmod m}a_{j}z^{j}$ where\n$m\\in\\mathbb{N}$ and $0\\le r<m$. We find conditions under which the zeros of\n$f_{r}(z)$ lie on $m$ radial rays defined by $\\Im z^{m}=0$ and $\\Re z^{m}\\le0$.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"47 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Entire functions with an arithmetic sequence of exponents\",\"authors\":\"Dallas Ruth, Khang Tran\",\"doi\":\"arxiv-2408.02096\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a given entire function $f(z)=\\\\sum_{j=0}^{\\\\infty}a_{j}z^{j}$, we study\\nthe zero distribution of $f_{r}(z)=\\\\sum_{j\\\\equiv r\\\\pmod m}a_{j}z^{j}$ where\\n$m\\\\in\\\\mathbb{N}$ and $0\\\\le r<m$. We find conditions under which the zeros of\\n$f_{r}(z)$ lie on $m$ radial rays defined by $\\\\Im z^{m}=0$ and $\\\\Re z^{m}\\\\le0$.\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"47 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Complex Variables\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.02096\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.02096","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Entire functions with an arithmetic sequence of exponents
For a given entire function $f(z)=\sum_{j=0}^{\infty}a_{j}z^{j}$, we study
the zero distribution of $f_{r}(z)=\sum_{j\equiv r\pmod m}a_{j}z^{j}$ where
$m\in\mathbb{N}$ and $0\le r
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
