{"title":"一类快速收敛有理数级数的无理性指数","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":"{\"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}","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}
Irrationality exponents of certain fast converging series of
rational numbers
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