{"title":"Irrationality exponents of certain fast converging series of\n rational numbers","authors":"D. Duverney, T. Kurosawa, I. Shiokawa","doi":"10.21099/TKBJM/20204402235","DOIUrl":null,"url":null,"abstract":"Let {xn} be a sequence of rational numbers greater than one such that xn+1 ≥ xn for all sufficiently large n and let εn ∈ {−1, 1}. Under certain growth conditions on the denominators of xn+1/x 2 n we prove that the irrationality exponent of the number ∑∞ n=1 εn/xn is equal to lim supn→∞(log xn+1/ log xn). 2010 Mathematics Subject Classification: 11A55, 11J70, 11J82, 11J91","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/TKBJM/20204402235","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let {xn} be a sequence of rational numbers greater than one such that xn+1 ≥ xn for all sufficiently large n and let εn ∈ {−1, 1}. Under certain growth conditions on the denominators of xn+1/x 2 n we prove that the irrationality exponent of the number ∑∞ n=1 εn/xn is equal to lim supn→∞(log xn+1/ log xn). 2010 Mathematics Subject Classification: 11A55, 11J70, 11J82, 11J91