关于多元超越全函数的例外集

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2023-10-20 DOI:10.1017/s0004972723001041

DIEGO ALVES, JEAN LELIS, DIEGO MARQUES, PAVEL TROJOVSKÝ

{"title":"关于多元超越全函数的例外集","authors":"DIEGO ALVES, JEAN LELIS, DIEGO MARQUES, PAVEL TROJOVSKÝ","doi":"10.1017/s0004972723001041","DOIUrl":null,"url":null,"abstract":"Abstract We prove that any subset of $\\overline {\\mathbb {Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountably many transcendental entire functions over $\\mathbb {C}^m$ with rational coefficients. This result solves a several variables version of a question posed by Mahler for transcendental entire functions [ Lectures on Transcendental Numbers , Lecture Notes in Mathematics, 546 (Springer-Verlag, Berlin, 1976)].","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"2 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON THE EXCEPTIONAL SET OF TRANSCENDENTAL ENTIRE FUNCTIONS IN SEVERAL VARIABLES\",\"authors\":\"DIEGO ALVES, JEAN LELIS, DIEGO MARQUES, PAVEL TROJOVSKÝ\",\"doi\":\"10.1017/s0004972723001041\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove that any subset of $\\\\overline {\\\\mathbb {Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountably many transcendental entire functions over $\\\\mathbb {C}^m$ with rational coefficients. This result solves a several variables version of a question posed by Mahler for transcendental entire functions [ Lectures on Transcendental Numbers , Lecture Notes in Mathematics, 546 (Springer-Verlag, Berlin, 1976)].\",\"PeriodicalId\":50720,\"journal\":{\"name\":\"Bulletin of the Australian Mathematical Society\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-10-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Australian Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/s0004972723001041\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Australian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s0004972723001041","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要证明了$\overline {\mathbb {Q}}^m$的任意子集(闭于复共轭且包含原点)是$\mathbb {C}^m$上具有有理系数的无数超越整函数的例外集。这个结果解决了由Mahler提出的关于超越全函数的几个变量版本的问题[关于超越数的讲座，数学讲义，546 (Springer-Verlag，柏林，1976)]。

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

ON THE EXCEPTIONAL SET OF TRANSCENDENTAL ENTIRE FUNCTIONS IN SEVERAL VARIABLES

Abstract We prove that any subset of $\overline {\mathbb {Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountably many transcendental entire functions over $\mathbb {C}^m$ with rational coefficients. This result solves a several variables version of a question posed by Mahler for transcendental entire functions [ Lectures on Transcendental Numbers , Lecture Notes in Mathematics, 546 (Springer-Verlag, Berlin, 1976)].

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

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society