{"title":"Frobenius集合上的加权Sylvester和","authors":"T. Komatsu, Yuancao Zhang","doi":"10.33232/bims.0087.35.44","DOIUrl":null,"url":null,"abstract":"Let $a$ and $b$ be relatively prime positive integers. In this paper the weighted sum $\\sum_{n\\in{\\rm NR}(a,b)}\\lambda^{n-1}n^m$ is given explicitly or in terms of the Apostol-Bernoulli numbers, where $m$ is a nonnegative integer, and ${\\rm NR}(a,b)$ denotes the set of positive integers nonrepresentable in terms of $a$ and $b$.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"155 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":"{\"title\":\"Weighted Sylvester sums on the Frobenius set\",\"authors\":\"T. Komatsu, Yuancao Zhang\",\"doi\":\"10.33232/bims.0087.35.44\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $a$ and $b$ be relatively prime positive integers. In this paper the weighted sum $\\\\sum_{n\\\\in{\\\\rm NR}(a,b)}\\\\lambda^{n-1}n^m$ is given explicitly or in terms of the Apostol-Bernoulli numbers, where $m$ is a nonnegative integer, and ${\\\\rm NR}(a,b)$ denotes the set of positive integers nonrepresentable in terms of $a$ and $b$.\",\"PeriodicalId\":103198,\"journal\":{\"name\":\"Irish Mathematical Society Bulletin\",\"volume\":\"155 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"19\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Irish Mathematical Society Bulletin\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33232/bims.0087.35.44\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Irish Mathematical Society Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33232/bims.0087.35.44","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let $a$ and $b$ be relatively prime positive integers. In this paper the weighted sum $\sum_{n\in{\rm NR}(a,b)}\lambda^{n-1}n^m$ is given explicitly or in terms of the Apostol-Bernoulli numbers, where $m$ is a nonnegative integer, and ${\rm NR}(a,b)$ denotes the set of positive integers nonrepresentable in terms of $a$ and $b$.