{"title":"A note on the Wiman-Valiron inequality","authors":"Karl-G. Grosse-Erdmann","doi":"arxiv-2409.06499","DOIUrl":null,"url":null,"abstract":"The Wiman-Valiron inequality relates the maximum modulus of an analytic\nfunction to its Taylor coefficients via the maximum term. After a short\noverview of the known results, we obtain a general version of this inequality\nthat seems to have been overlooked in the literature so far. We end the paper\nwith an open problem.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"70 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","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-2409.06499","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The Wiman-Valiron inequality relates the maximum modulus of an analytic
function to its Taylor coefficients via the maximum term. After a short
overview of the known results, we obtain a general version of this inequality
that seems to have been overlooked in the literature so far. We end the paper
with an open problem.
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