{"title":"关于Hardy-Littlewood素数元组猜想和Ramanujan和的高卷积","authors":"Sneha Chaubey, Shivani Goel, M. Ram Murty","doi":"10.7169/facm/2048","DOIUrl":null,"url":null,"abstract":"We introduce the study of triple convolution Ramanujan sums and apply it to give a~heuristic derivation of the Hardy-Littlewood conjecture on prime 3-tuples without using the circle method. We also estimate the triple convolution of the Jordan totient function using Ramanujan sums.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Hardy-Littlewood prime tuples conjecture and higher convolutions of Ramanujan sums\",\"authors\":\"Sneha Chaubey, Shivani Goel, M. Ram Murty\",\"doi\":\"10.7169/facm/2048\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the study of triple convolution Ramanujan sums and apply it to give a~heuristic derivation of the Hardy-Littlewood conjecture on prime 3-tuples without using the circle method. We also estimate the triple convolution of the Jordan totient function using Ramanujan sums.\",\"PeriodicalId\":44655,\"journal\":{\"name\":\"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7169/facm/2048\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7169/facm/2048","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Hardy-Littlewood prime tuples conjecture and higher convolutions of Ramanujan sums
We introduce the study of triple convolution Ramanujan sums and apply it to give a~heuristic derivation of the Hardy-Littlewood conjecture on prime 3-tuples without using the circle method. We also estimate the triple convolution of the Jordan totient function using Ramanujan sums.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
